Surface stabilized ferroelectric liquid crystal devices

ABSTRACT

A liquid crystal device including a ferroelectric liquid crystal disposed between plates treated to enforce a particular ferroelectric molecular orientation to the plates. The devices employ alone or in combination non-planar boundary conditions, polar boundary conditions, boundaries with multiple physical states, intrinsic spontaneous splay distortion of the polarization orientation field, combined ferroelectric and dielectric torques, layers tilted with respect to the plates. The plates are spaced by a distance sufficiently small to ensure unwinding of the helix typical in a bulk of the material to form either monostable, bistable or multistable states which exhibit novel electro-optic properties. The liquid crystal is responsive to an externally applied electric field, temperature or the like to make a light valve or other electro-optical device.

This is a continuation of pending application Ser. No. 07/969,386, filedOct. 30, 1992, which is a continuation of application Ser. No.07/826,473, filed Jan. 27, 1992, and issued as U.S. Pat. No. 5,227,905;which is a cont. of application Ser. No. 491,464, filed Mar. 9, 1990,issued as U.S. Pat. No. 5,083,855; which is a div. of application Ser.No. 318,762, filed Mar. 3, 1989, and issued as U.S. Pat. No. 4,958,916;which is a div. of application Ser. No. 225,464, filed Jul. 28, 1988,and issued as U.S. Pat. No. 4,840,463; which is a div. of applicationSer. No. 88,482, filed Aug. 19, 1987 issued as U.S. Pat. No. 4,813,767;which is a cont. of application Ser. No. 797,021, filed Nov. 12, 1985,now abandoned; which is a div. of application Ser. No. 511,733, filedJul. 7, 1983, and issued as U.S. Pat. No. 4,563,059; which is acont.-in-part of application Ser. No. 456,844, filed Jan. 10, 1983, nowabandoned; which is a cont. of application Ser. No. 110,451, filed Jan.8, 1980, and issued as U.S. Pat. No. 4,367,924.

TABLE OF CONTENTS

I. BACKGROUND OF THE INVENTION

A. Field of the Invention

B. U.S. Pat. No. 4,367,924

C. Achieving Layer and Director Alignment

D. Ferroelectric Liquid Crystals

II. SUMMARY OF THE INVENTION

III. BRIEF DESCRIPTION OF THE DRAWING

IV. BOUNDARY CONDITIONS

A. Introduction

B. Conical Boundary Conditions

1. Complete Conical Boundary Conditions

a. Circular Conical Boundary Conditions

b. Anisotropic Conical Boundary Conditions

2. Incomplete Conical Boundary Conditions

C. Polar Boundary Conditions

D. Boundary Surfaces with Multiple Physical States

V. NORMAL LAYER GEOMETRY

A. Circular Conical Boundary Conditions

B. Anisotropic Conical Boundary Conditions

C. Incomplete Conical Boundary Conditions

D. Polar Boundary Conditions

VI. TILTED LAYER GEOMETRY

VII. INTRINSIC SPLAY OF THE POLARIZATION FIELD

VIII. COMBINED FERROELECTRIC AND DIELECTRIC TORQUES

IX. DEVICE STRUCTURES AND DEVICE STATES

A. Introduction

B. Devices Employing Circular Conical (C--C) Boundary Conditions

1. N--C² Structures

2. N--C₁ C₂ Structures

C. Devices Employing Unsymmetric Conical (U--U) Boundary Conditions

1. N--U² Structures

2. N--U₁ U₂ Structures

D. Devices Employing Mixed Circular Conical and Unsymmetric AnisotropicConical (C--U) Boundary Conditions

E. Devices Employing Tilted Layers (T)

F. Devices Employing Polar (P) Boundary Conditions

G. Devices Employing Combinations of Ferroelectric and DielectricTorques

H. Device Variations

1. Boundary and Layer Tilt Conditions Approximating Those of U.S. Pat.No. 4,367,924

2. Devices with Pretilt

3. Devices with Nonhomogeneous Bounding Plates

4. Devices Employing Temperature as a Variable Parameter

X. EXAMPLES OF SSFLC DEVICES

A. Introduction

B. Applications of Devices Employing Two-State Pixels

1. Device in U.S. Pat. No. 4,367,924

2. Non-Emissive Screens

3. Color Devices

C. Devices with Multiple State Pixels

1. Twisted Smectic Devices

2. Other Multiple State Devices

D. Non-Matrix Arrays

E. Design and Fabrication of Cells

XI. CLAIMS

I. BACKGROUND OF THE INVENTION

A. Field Of The Invention

This application relates to liquid crystal devices, particularly devicesemploying ferroelectric liquid crystals.

B. U.S. Pat. No. 4,367,924

In U.S. Pat. No. 4,367,924 (hereinafter "said patent"), the contents ofwhich are incorporated herein by reference, a liquid crystalelectro-optic device is described employing a chiral smectic C or Hferroelectric liquid crystal. In that device the liquid crystal isdisposed between parallel plates with the planar smectic layers normalto the plates (see said patent, FIG. 2). These smectics arecharacterized by an average molecular long axis direction, indicated bythe molecular director, n, which is constrained, in equilibrium, to makesome temperature dependent angle, Ψ_(o), with the normal to the layers,but which is free to take up any value of the angle φ which gives theorientation of n about the layer normal. Typically Ψ_(o), which is aproperty of the bulk smectic, is in the range from 0° to about 45°. Theferroelectric polarization, P, reorients with n, always remaininglocally normal to n and lying parallel to the plane of the lavers, asshown in FIGS. 1 and 2 of said patent.

In the device described in said patent, the plates were treated so thatthe molecules near the plates would adopt an orientation having theaverage molecular long axis direction parallel to the plane of theplates but free to adopt any orientation within that plane. That is, themolecular director, n, is constrained at the surface to lie in thesurface plane. This condition, when combined with the additionalconstraint that the director make the angle Ψ_(o) with the normal to thelayers (see said patent, FIG. 2), leads to a geometry in which, if theplates are sufficiently close together, the intrinsic helicalconfiguration of n which is present in the bulk will be suppressed,leaving two surface stabilized states of the molecular orientationconfiguration, each having the ferroelectric polarization normal to theplates but in opposite directions (see said patent, FIG. 2). Devicessuch as this, which employ surface interactions to stably unwind thespontaneous ferroelectric helix, will be referred to as SurfaceStabilized Ferroelectric Liquid Crystal (SSFLC) devices.

The device of said patent exhibits several novel features whichdistinguish it from other liquid crystal devices:

(1) Optic axis rotation about the sample normal--A ferroelectric smecticin this geometry behaves optically as a biaxial slab with the optic axesnearly along the director orientation. The biaxiality is generally weak,so the behavior is essentially uniaxial with the uniaxis along thedirector. The effect of switching is to rotate the uniaxis about thenormal to the surface through an angle of twice the tilt angle Ψ_(o).This is the only liquid crystal parallel-plate geometry allowing arotation of the uniaxis of a homogenous sample about the surface normal.

(2) Strong-weak boundary conditions--Another unique feature to be notedis the nature of the required boundary condition. In order to obtainbistability, boundary conditions which constrain the molecules to beparallel to the plates but allow several or continuous orientationsabout the normal to the plates are required. The device of said patentis the first liquid crystal electro-optic structure to employ such acombination of strong and weak boundary conditions. A consequence ofthis feature and an essential property of the structure is that thedirector at the surfaces is switched between stable surface orientationstates as an intrinsic part of the overall switching process. The SSFLCis the first liquid crystal electro-optic structure wherein switchingbetween stable surface states has been demonstrated and the first casein which ferroelectric liquid crystal domains have been made to appear.

(3) A significantly higher switching speed--As a result of having thehelix unwound, it is the first ferroelectric liquid crystal device toachieve the minimum, intrinsic response time for molecular reorientationto a changing electric field, since, with the helix unwound, bulkreorientation can occur without the motion of topological defects in theorientation field.

C. Achieving Layer and Director Alignment

An indispensable requirement necessary to make a practical electro-opticdevice using the surface stabilized ferroelectric liquid crystalgeometry is to achieve, in the ferroelectric smectic phase, both thedesired director boundary condition and the desired layer orientation ina uniform fashion over the entire active device area. Boundaryconditions influencing the director orientation at the surface areestablished by specific surface preparations. Possible boundaryconditions and their properties in the surface stabilized ferroelectricliquid crystal geometry are discussed in detail in the next section.Uniform layer orientation, on the other hand, must be established bysome specific step appropriately controlling the growth or arrangementof the smectic layers in the process of fabricating the liquid crystalcell.

Excluding the geometry having the liquid crystal layers parallel to theplates, which is not of relevance to this application, there are onlythree ways demonstrated in the art of achieving uniform layerorientation of a smectic C or a tilted smectic crystal. The first arethe well-known anisotropic surface treatment techniques of rubbing oroblique SiO evaporation, combined with the smectic A--C transition, asreviewed by K. Kondo et al in the Japanese Journal of Applied Physics,Volume 20, pp. 1773-1777, 1981. The other two are the combination ofexternal shear and the smectic A--C transition described in said patent,and the combination of magnetic field and the smectic A--C transition,also described in said patent and since reported by K. Kondo et al, op.cit. Using the nematic to smectic C transition has not proven successfulin achieving homogeneous layer alignment, since even the strong surfaceplanar alignment provided by oblique evaporation of silicon monoxide,which fixes the director orientation in space, produces two differentlayer orientations in distinct regions, as has been demonstrated by M.Brunet, Le Journal de Physique, Volume 36, pp. C1, 321-324, 1975, and G.Peltzl et al., Molecular Crystals and Liquid Crystals, volume 53,167-180, 1979.

All of the above-mentioned treatments involve ordering in one phase andcooling into the smectic C phase. They involve a combination ofprocesses and are thus complicated compared to, for example, thealignment process for twisted nematic cells, which requires only surfacetreatment. It would be desirable to have available processes foralignment of layers in ferroelectric smectics which involve only surfacetreatment (and perhaps the use of a phase transition) which providecontrollable surface orientation characteristics for the director in theferroelectric smectic phase. In Section X E, techniques are discussedfor layer orientation of ferroelectric liquid crystals and a novelmethod is introduced involving two kinds of boundary condition, oneacting upon the director, the other upon the layer.

D. Ferroelectric Liquid Crystals

In said patent, an electro-optic device employing a ferroelectricsmectic C or H liquid crystal was described. The features of theseferroelectric phases essential to the operation of the device are: (1)they are smectics in which the rod shaped molecules are arranged intolayers with the director tilted at some angle relative to the normal tothe lavers; (2) the molecules are chiral, producing, according to thearguments of Meyer et al (Le Journal de Physique, Volume 36, pp.,L69-71, 1975), a bulk ferroelectric dipole moment, P, normal to n. Thechiral compounds discussed in the original application, DOBAMBC andHOBACPC, have several tilted smectic--and thereforeferroelectric--phases, two of which were identified at the time of theapplication: the smectic C phase over some temperature range and, atlower temperatures, a phase which we described as smectic H in accordwith the identifications made by the group that synthesized thecompounds (P. Keller et al, Le Journal de Physique, Volume 37, pp.C3-27, 1976). However, other data (J. Doucet, et al, Le Journal dePhysique, Volume 39, pp. 548-553, 1978) suggested that there are atleast two phases below the smectic C in HOBACPC, a smectic F (now calledsmectic I) adjacent to the C, and a smectic H at lower temperatures.More recent heat capacity studies by the inventors confirm the latterdata. The nomenclature of the various tilted smectic phases has beensubject to some changes in the last two years and both theircrystallographic identification and nomenclature is in a state ofconsiderable flux.

The presently adopted distinction among the five ferroelectric smecticphases now identified with certainty--smectics C,F,G,H,I--is as follows.The smectic C phase is the most fluid, having normal liquid state orderwithin a given layer, i.e., local positional order involving only a fewmolecules. The smectic F and I phases have considerably more order in agiven plane, with typically hundreds of molecules grouped into localquasi-crystalline regions. This leads to an orientational viscosity ofthe smectic F and I which is about 100 times that of the smectic C. Thesmectic F and I are distinguished by the different orientation of thetilt direction relative to the local crystal lattice direction. Thesmectic G and H phases are much more strongly ordered, with nearly longrange (quasi-crystalline) translational ordering in a given layer, andvery high viscosities. New subdivisions of the G and H classes,necessitating the further denominations J and K, have recently beenproposed.

However, the crystallographic details of internal ordering add nothingnew in principle. All chiral tilted smectics are ferroelectric andalthough the original application discussed specifically the smectic Cand H phases (now identified as C and I in HOBACPC and C and F inDOBAMBC), we point out here that devices like that of said patent orlike those to be described in this application may employ any of theseferroelectric phases and operate in essentially the same fashion. Therewill be qualitative features of the various phases that will dictatewhich to use in a particular situation. For example, as one proceedsfrom the least to the most strongly ordered, the electro-optic switchingmay become slower but with improved stability (memory, threshold)characteristics of the switching. Also, as the correlation betweensmectic layers grows stronger, the helix pitch will increase (becominginfinite in the limit of sufficiently strong ordering), allowing thicksamples to be switched bistably.

II. SUMMARY OF THE INVENTION

In this application, new ferroelectric liquid crystal devices aredescribed which have the same basic SSFLC geometry as that of saidpatent, i.e., a ferroelectric smectic liquid crystal introduced betweenplates such that: (1) the electric polarization can couple to anelectric field applied across the plates. This implies that the layersare planar and normal to a specific direction over the entire sample,and that they make some angle substantially greater than zero with thebounding plates. In the device of said patent they were perpendicular tothe bounding plates, but this application goes beyond the condition ofstrict perpendicularity for certain purposes to allow a well-defined andspecified tilt; (2) the liquid crystal layer is sufficiently thin thatsurface interactions stably unwind the intrinsic helix.

These new devices differ from that of said patent in that they employ,alone or in combination: NON-PLANAR boundary conditions; POLAR boundaryconditions; boundaries with multiple physical states; intrinsicspontaneous splay distortion of the polarization orientation field;combined ferroelectric and dielectric torques; layers tilted withrespect to the bounding surface planes; and in order to produceferroelectric smectic structures with monostable, bistable, ormultistable states which exhibit novel and useful electro-opticproperties.

These new devices share with the device of said patent the followingimportant advantages of the SSFLC geometry in electro-opticapplications: (1) a significant component of the electric field-induceddirector rotation is normal to the plane of the bounding surface; (2)the response time for electric field-induced molecular reorientation isminimized, being determined by intrinsic orientational viscosity, andnot by the field-induced elimination of long lived topological defects.

It should also be noted that either these or the device of said patentcan employ any of the ferroelectric liquid crystal phases.

FIG. 1 illustrates the geometry relevant to our description. The smecticlayers such as layer 100 are planes taken to be parallel to the x,yplane, the layer normal being z. The x,y axes are oriented so that x isparallel to the line of intersection of the layers with the boundingsurface. Indicated in FIG. 1 is n, with its sign always chosen so thatn·z>0. Note that, although the director n is commonly written in the artas a vector, there is no physical significance attached to its sign,that is n and -n describe the same physical state, so that n can berepresented by a line segment (said patent, FIGS. 1 and 2). Alsoindicated is the unit vector parallel to the projection of n on thelayer plane, c, and the ferroelectric polarization, P=P(zxn), which isalways mutually perpendicular to both n and c. Two collinear directions,depending on the sign of P, are thus possible for P, and examples ofeach kind are known in the art. If P>0 for a certain substance, then z,n, and P form a right-handed coordinate system and we have a (+)substance with regard to polarization. If P<0, they form a left-handedsystem, as the one in the figure, and we have a (-) substance. Theconcrete examples of compounds most often cited in this and the originalapplication, DOBAMBC and HOBACPC, both belong to the (-) class, andsubsequent figures in this and said patent exemplify the situation forthese compounds, regarding the spatial relationship of n and P. Theangle between n and z is Ψ, and the angle between n and the normal tobounding surface 102, s, is Ω. The angle δ gives the tilt of smecticlayers 100 away from being normal to plates 102, i.e., δ is the anglebetween z and the surface of bounding plate 102. The angle α is betweenx and n_(s), the projection of n onto the bounding surface 102.

FIG. 2 indicates, for a (+) substance (a) and a (-) substance (b), theprojection of n and P on the layer (x,y) plane 104, showing also c andthe intersection of the layer with surface bounding plates 106 and 108.The mutually perpendicular vectors, P and c, are constrained to lieparallel to the x,y (layer) plane so that any possible P-c reorientationcan be described by the single angle φ between x and c. A constantelectric potential difference across the bounding plates produces anelectric field E, parallel to s, whose component along the y axis E_(y)=yE cos δ makes an angle φ with the P of a (+) substance. If, as in saidpatent, the layers are perpendicular to the plates (s≡-y, δ=0), thenE_(y) =E, and the layer width along y is just the liquid crystal layerthickness, d. Since n is not parallel to the plane of the paper, a shortbar is added to the end of n which is up out of the paper toward thereader.

III. BRIEF DESCRIPTION OF THE DRAWING

These and other objects and advantages of the invention will become moreapparent and more readily appreciated from the following detaileddescription of the presently preferred exemplary embodiment of theinvention taken in conjunction with the accompanying drawings, of which:

FIG. 1 is a schematic representation of a liquid crystal and associatedboundary surface;

FIGS. 2a and 2b are schematic representations of chiral (+) and chiral(-), bounded liquid crystals;

FIGS. 3a-3e are schematic representations of boundary conditions andcorresponding polar diagrams of surface energy;

FIGS. 4a and 4b are schematic representations of the effect on liquidcrystal material of circular conical boundary conditions;

FIG. 5 is a schematic representation of the effect on liquid crystalmaterial of tilted circular boundary conditions;

FIGS. 6a and 6b are schematic representations of surface orientationsadopted with POLAR boundary conditions;

FIGS. 7a-7d are schematic representations of the effect on liquidcrystal material with layers tilted from the normal to the boundaries;

FIG. 8a is a schematic representation of intrinsic polarization splay ina liquid crystal;

FIG. 8b is a schematic representation of a device in which the liquidcrystal polarization field is splayed;

FIGS. 9a-9c are schematic representations of devices with identicalCIRCULAR CONICAL boundary conditions;

FIGS. 10a and 10b are schematic representations of devices withdiffering CIRCULAR CONICAL boundary conditions;

FIGS. 11a and 11b are schematic representations of devices withidentical UNSYMMETRIC CONICAL boundary conditions;

FIGS. 12a and 12b are schematic representations of devices withdiffering UNSYMMETRIC CONICAL boundary conditions;

FIGS. 13a and 13b are schematic representations of devices withdiffering UNSYMMETRIC CONICAL boundary conditions with each aligningmeans having a different direction of anisotropy;

FIGS. 14a and 14b are schematic representations of devices with aCIRCULAR CONICAL and an UNSYMMETRIC ANISOTROPIC boundary condition;

FIGS. 15a-15d are schematic representations of devices with tiltedlayers;

FIG. 16 is a schematic, exploded representation of a transmissiveelectro-optical device according to the present invention;

FIG. 17 is a schematic, exploded representation of a reflectiveelectro-optical device according to the present invention;

FIG. 18 is a diagram for explaining the operation of the device in FIG.17;

FIG. 19 is a schematic, exploded representation of a reflectiveelectro-optical device with a polarizer behind the liquid crystal;

FIGS. 20a, 20c and 20d represent schematic diagrams of possiblemultithickness devices;

FIG. 20b is a side elevation view of the device schematically depictedin FIG. 20c;

FIGS. 21a and 21b are representations of devices having two liquidcrystal layers between three aligning means having two pairs ofelectrodes;

FIGS. 22a and 22b are schematic representations of devices having twoliquid crystal layers wherein a single electric field is applied;

FIG. 23 is a schematic representation of a device with differentboundary conditions on the two surfaces;

FIGS. 24a and 24b are schematic representations of a device withdifferent switching thresholds at the top and bottom surfaces;

FIG. 25 is a schematic representation of a device which combines theoutput of several pixels with optics;

FIGS. 26a and 26b are schematic representations of a device in which theelectric field is applied parallel to the boundary glass plates;

FIGS. 27a, 27b and 28 are schematic representations of a deviceemploying temperature variations to establish additional states; and

FIGS. 29 and 30 are schematic representations of devices employingpatterned, electrode and surface treatment areas.

IV. BOUNDARY CONDITIONS

A. Introduction

Discussed herein are molecule-surface interactions which exert torqueson the molecules, and therefore on the director, in the vicinity of thesurface. These interactions are said to establish some boundarycondition on the director. Interactions which are known in the art toproduce such torques are: (1) chemical bonding (e.g. covalent orhydrogen bonding) of liquid crystal and surface molecules or groups,which acts only on molecules in contact with the surface; (2)dipole-induces dipole interactions (anisotropic Van der Waalsinteractions) which will influence a layer of finite thickness at thesurface; (3) electrostatic interactions, such as the electrostaticrepulsion of the permanent liquid crystal molecular dipoles from asurface of dielectric constant lower than that of the liquid crystal;(4) steric interactions, i.e. a particular surface orientation mayproduce more efficient packing of the molecules near the surface; (5)macroscopic elastic effects, such that, for example, the director at thesurface will rotate to minimize distortion of the director field.

It is common in the art to characterize the "strength" of the surfaceforces by measuring or calculating the surface energy per unit area,F_(s) (Ω, α), associated with a particular orientation of the directorat the surface, Ω (0°<Ω<90°) being the angle between n and the surfacenormal, and α(0° <α<360°) the angle between x and n_(s) the projectionof n onto the surface plane (see FIG. 1). Surface torques are obtainedby calculating appropriate derivatives of F_(s) with respect to Ω and α.For common liquid crystal devices both Ω and α are free variables, i.e.they are free to adopt whatever combination of Ω and α that willminimize F_(s) (Ω, α). For the devices to be described here, however,the allowed orientations of n will be subject to the additionalconstraint of a preferred tilt angle, Ψ_(o), relative to the normal tothe smectic layers. Thus, it is necessary to consider the surfaceenergetics with a constraint applied to n. We will consider thevariation of F_(s) (Ω, α) vs Ω for α fixed, the equilibrium (preferred)angles, Ω_(o) (α), being those for which F_(s) is a local minimum withrespect to Ω, having the value F_(s) (Ω_(o) (α),α)=F_(min) (α). Forboundary conditions known in the art, F_(s) (Ω,α) has at most one localminimum for a given α for Ω in the range 0°<Ω<90°. FIGS. 3a-3e showpolar diagrams of several possible F_(s) (Ω,α)'s, corresponding todifferent constraint conditions for n. Here F_(s) (α) is plottedadjacent to F_(s) (α+180°) since the constraint planes for these two α'sare identical, and F_(s) (Ω,α) continues smoothly into F_(s) (Ω,α+180°).For a given α, external torques, arising from applied fields or fromnonuniformity of the director field, are required to change Ω from oneof its equilibrium values of Ω_(o) (α).

B. CONICAL Boundary Conditions

The equilibrium condition for the director at a bounding plate can berepresented by a boundary orientational constraint surface which is thegeneralized conic surface swept out by a line making the angle Ω_(o) (α)with the surface normal as α is increased from 0° to 360°. Examples ofpossible such boundary constraint surfaces 110, corresponding to theindicated F_(s) (Ω,α), are shown in FIGS. 3a-3e and will be discussed inthe following sections. In general, there are two distinct classes ofboundary conditions: COMPLETE CONICAL boundary conditions, asexemplified by FIGS. 3a-3d, in which the boundary constraint surfaceexists in the entire range 0°>α>360°, i.e., there is local minimum inF_(s) for each α, and INCOMPLETE CONICAL boundary conditions, asexemplified by FIG. 3e, in which the boundary constraint surface existsfor only part of the α range. These cases will now be discussed in turn:

1. COMPLETE CONICAL Boundary Conditions

a) CIRCULAR CONICAL Boundary Conditions (FIG. 3a)--A particularly simplecase of CONICAL boundary conditions are CIRCULAR CONICAL boundaryconditions, for which, in the absence of external torques, the directorcan take any orientation on a cone of angle Ω_(o), coaxial with thesurface normal. Special cases of CIRCULAR CONICAL boundary conditionsare the usual homeotropic boundary conditions for which Ω_(o) =0°(director normal to the surface), and the boundary conditions of saidpatent, Ω_(o) =90°. The general CIRCULAR CONICAL boundary condition isknown in the art (for example, see G. Ryschenkov and M. Kleman, Journalof Chemical Physics, Volume 64, pp. 404-412, 1976, and E.Dubois-Violette and P. G. deGennes, Le Journal de Physique, volume 36,pp. L255-258, 1975).

The simplest expression for F_(s) yielding CIRCULAR CONICAL boundaryconditions is F_(s) =4Γ[1-{(sin Ω sin Ω_(o))² +(cos Ω cos Ω_(o))² }],which is minimum for Ω=Ω_(o) and which has four maxima as Ω varies from0° to 360°. For the case of the device of said patent (Ω_(o) =90°),F_(s) reduces to F_(s) =4Γ(cos Ω)². The strength of the surfaceinteraction depends on the magnitude of the surface energy anisotropyparameter, Γ. The larger Γ is, the larger will be the surface torquesconstraining Ω to be Ω_(o), all else being equal.

CIRCULAR CONICAL boundary conditions with Ω_(o) =90° can be created byusing clean glass to contain the liquid crystal. Ω_(o) can be varied byadding a thin hydrocarbon layer on the glass. As the thickness of thehydrocarbon layer varies, Ω_(o) will vary.

b) ANISOTROPIC CONICAL Boundary Conditions (FIGS. 3b-d)--It is alsopossible to make CONICAL boundary conditions which are anisotropic inthe bounding surface plane, by introducing anisotropy into surfacetreatments which would otherwise produce CIRCULAR CONICAL boundaryconditions. Such ANISOTROPIC CONICAL boundary conditions may beclassified according to the point group symmetry of their boundaryconstraint surface. For example, a weak bidirectional rubbing of thesurface to establish a special surface direction before deposition ofthe thin hydrocarbon layer according to Ryschenkov (op. cit.) wouldproduce a surface state characterized by the point group symmetry 2 mm,which could be simply represented by the elliptical cone of FIG. 3b.Alternatively, the thin hydrocarbon layer could be applied withmolecules oriented in a predetermined manner. One of the two mirrorplanes would be parallel to, and the other perpendicular to, the specialdirection. In a similar way, unidirectional rubbing or obliqueevaporation of material onto the surface would lead to a surface statecharacterized by the point group symmetry m, for instance exemplified bythe oblique circular cone in FIG. 3c, the axis of which is rotated awayfrom the surface normal by the polar angle β in the direction given bythe azimuthal angle, α. In the general case, as exemplified by theboundary constraint surface in FIG. 3d, the surface state will not besymmetric under any point operations.

Different symmetries are possible with the liquid crystal applied"epitaxially" on a clean crystal solid surface. Thus, if the crystalsolid surface is hexagonally arranged, "grooves" in three directions arecreated, thus creating threefold symmetries with the liquid crystal.

2. INCOMPLETE CONICAL Boundary Conditions

For some surface treatments there will be a local minimum of F_(s) (Ω,α)vs Ω for only a finite range of α. An example of such a boundaryconstraint surface is indicated in FIG. 3e. This boundary constraintsurface, which could be obtained by slightly oblique evaporation of SiO,has the favored director tilt at the surface of Ω_(o) (0) for theevaporation direction plane (α=0). The angle α=0 is the angle of minimumF_(s) (α), so that the otherwise unconstrained director would adopt theorientation Ω_(o) (0), α=0 at the surface. In the smectic C, satisfyingthe layer constraint cone can force α to be nonzero with the result ofchanging Ω_(o) (α), up to some maximum α=α_(m), at which the localminimum in F_(s) disappears. An attempt to increase α beyond this valuewould result in the director effectively flipping 180° in α, to α+180°,which is again less than α_(m).

C. POLAR Boundary Conditions

The liquid crystal-surface interaction can possess components whichfavor POLAR boundary conditions in addition to components favoringCONICAL. Considered here are interactions between the surface and theferroelectric polarization, which orient the molecules at the surface tofavor a particular orientation of the component of P normal to thesurface, i.e. either into or out of the surface. To cite an example ofsuch an interaction, a surface covered with discrete dipoles directedaway from the surface would tend to align P at the surface in the samedirection.

The present inventors have discovered cases where the ferroelectricliquid crystal favors an orientation either into or out of the surfacefor the component of the ferroelectric polarization vector normal to thesurface. That is, the interaction of a particular surface treatment witha particular compound may prefer the ferroelectric polarization vectorat the surface to be directed out of the liquid crystal region and intothe surface material region. For example, it has been found that theferroelectric smectic C liquid crystals,S-4-(6-methyl)octyl-resorcylidene-4'-octylaniline, or bis(S,S-4'-(6-methyl)-octyloxybenzylidene)-2-chloro-1,4-phenylenediamine,when in contact with a clean indium tin oxide coated glass surface,adopts this kind of a polar orientation of the ferroelectricpolarization near the interface. Alternatively, molecules with largedipole moments may be chemically attached to glass plates. Similarly,glass plates may be dipped in acid or base to create dipoles at thesurface of the glass. Finally, a liquid may be doped with a highlypolarized molecule which can adsorb onto glass plates. The direction ofpolarization depends on the kind of glass and liquid used.

D. Boundary Surface With Multiple Physical States

When the liquid crystal is applied "epitaxially" on a cleancrystallographic solid surface, molecule-crystal interactions canproduce specific director orientation at the surface. Moreover, theboundary can be active in the sense that the surface condition mayitself be switchable, for instance when the crystal surface belongs to asolid having a switchable structural transition, such as a crystallineferroelectric. Changing the state of the solid switchable surface willgenerally give rise to an increased number of optically distinct statesfor the cell as a whole. Thus, it is well-known from studies of MBBA onTriglycine Sulphate (M. Glogarova, Le Journal de Physique, Volume 42,pp. 1569-1574, 1981), that the nematic director of the MBBA orientsalong the surface if applied on a cleavage plane of TGS, but with anappreciable angular difference (32°) if adjacent to a (+) or a (-)domain, respectively. The possibility of favoring one or the otherdirector orientation in the corresponding ferroelectric smectic caseadds a new interesting means of active addressing.

In addition, crystalline ferroelectric boundaries will produce electricfields in the bulk liquid crystal which will also act to orient themolecules (M. Glogarova, ibid.). This is especially useful in theferroelectric smectic case as the field interaction with the liquidcrystal polarization can be expected to be more powerful than innematics. This combination of liquid crystal and solid retroelectricwould combine the solid's strong polarization and stability with thefluidity and large optical response of the liquid crystal.

V. NORMAL LAYER GEOMETRY

A. CIRCULAR CONICAL Boundary Conditions

When the CIRCULAR CONICAL boundary condition is applied to the surfacestabilized ferroelectric liquid crystal geometry, the director near thesurface is under two constraints: it must lie on the surface circularcone of angle Ω_(o), the axis of which is normal to the surface, as inFIG. 3a; it must also lie on the layer cone of angle Ψ_(o), the axis ofwhich is normal to the layers. Surface cone of constraint 110, and layercone of constraint 112 of liquid crystal 114 are indicated in FIG. 4afor the case where smectic layers 104 are normal to bounding surfaceplanes 116 and 118. Simultaneous application of these two constraints ingeneral determines four allowed values of φ at each surface, i.e. fourphysically distinct allowed orientations of the director, 1, 2, 3, and 4shown in FIG. 4a, and in FIG. 4b(i), which indicates as a circle layerconstraint cone 112 with its axis normal to the plane of the paper, thedots giving the intersections with the surface constraint cone (top),and showing the four orientations of n along with their associatedpolarization vectors, P, projected onto a plane parallel to the smecticlayers (bottom). As mentioned above, n is indicated as being notparallel to the plane of the projection surface by adding a short bar tothe end of n which is up out of the surface. The dashed arrows indicatethe stable states of P at a given surface. Thus, between each dashedarrow orientation is a surface energy maximum.

Some particular examples will now be discussed in reference to FIG. 4bof the behavior at a single surface 116 arising from CIRCULAR CONICALboundary conditions and discussed later, in Section IX, combinations ofsimilar and different boundary conditions on the two surfaces. At asingle surface, phenomena to be observed can be divided into twoclasses, depending on whether Ω_(o) is smaller or larger than 90°-Ψ_(o)(see FIG. 4a). We discuss these cases in turn:

    90°-Ψ.sub.o <Ω.sub.o <90°          (i)

In this, the general case, cones 110 and 112 intersect and yield fourstable surface orientations as indicated in FIGS. 4a and 4b(i). Thesestates may be grouped according to whether P is directed toward (1 and2) or away from (3 and 4) the surface, or according to whether P_(x),the horizontal component of P, is directed left (2 and 3) or right (1and 4).

    Ω.sub.o =90°                                  (ii)

As Ω_(o) increases toward 90°, the allowed orientations rotate so as tomake P more normal to the bounding surface, so that, for example, theorientations of states 1 and 2 become more alike.

At Ω_(o) =90° surface cone 110 collapses to a plane, the intersections 1and 2 overlap so that states 1 and 2 become identical (1≡2), with Pnormal to the surface. Thus, the four initial states reduce to two, 1≡2and 3≡4, indicated in FIG. 4b(ii) and respectively numbered 5 and 6.These are the boundary conditions and states described in said patent.

    Ω.sub.o ≦90°-Ψ.sub.o               (iii)

As Ω_(o) decreases, P in the various states rotates further away frombeing normal to the surface, so that states 2 and 3 become more similar,as do states 1 and 4. For Ω_(o) =90°-Ψ_(o) cones 110 and 112 touch alongjust two lines of intersection, one coincident with the intersectionsgiving states 2 and 3, the other with the intersections giving states 1and 4. That is, states 2 and 3 are identical (2≡3), with the orientationφ=270°and 1 and 4 become identical with the orientation φ=90°, φ againbeing the angle between x and c. Note that these states, respectivelynumbered 7 and 8 and shown in FIG. 4b(iii), have the ferroelectricpolarization parallel to the surface.

If Ω_(o) <90°-Ψ_(o) cones 110 and 112 do not intersect so that theboundary and layer constraint cannot be simultaneously satisfied. As aresult, the weaker of the constraints will be violated, the systemresponse depending on the strength of the bulk forces maintainingΨ=Ψ_(o) relative to the surface forces maintaining Ω=Ω_(o). Observationsindicate that in general the forces maintaining the smectic C tilt angleare dominant, so that the smectic C tilt angle everywhere remains closeto Ψ_(o). If this is so, then the surface forces will rotate n in orderto make Ω as close to Ω_(o) as possible. The two orientations indicatedin FIG. 4b(iii), obtained for Ω_(o) =90°-Ψ_(o) (φ=90° and φ=270°)satisfy this condition as well. Under conditions where the surfaceforces dominate, these same two angles will be stabilized, with thedirector tilt angle increasing from Ψ_(o) to Ω_(o) as the surface isapproached.

B. ANISOTROPIC CONICAL Boundary Conditions

A key symmetry property governing the combination of surface stabilizedstates obtained and their electrical switchability (to be discussed-inSection IX) is the symmetry behavior of the boundary constraint surfaceunder the mirror reflection x -x. The behavior under this operation willnot only depend on the shape of the boundary constraint surface but alsoon the orientation of its point group symmetry directions relative tothe layer direction. Surfaces having ANISOTROPIC CONICAL boundaryconditions will, for purposes of this discussion, be divided into twoclasses, those symmetric under the operation x -x [SYMMETRIC ANISOTROPICCONICAL (S) ], and those not symmetric under this operation [UNSYMMETRICANISOTROPIC CONICAL (U)]. For example, the elliptical cone of FIG. 3bwill give boundary conditions (S) only if the mirror planes are parallelor perpendicular to the x direction. As a further example, tilting thecircular cone 110 as in FIG. 3c away from the surface normal in thedirection parallel to the smectic layers (γ=0), yields boundaryconditions -U-, in particular the set of states shown in FIG. 5. Notethat these states are obtained respectively from those of FIGS. 4b(i) to(iii) by rotating all of the states in the same direction through theangle β. This rotation eliminates the reflection symmetry about the y,zplane (x -x) present in the states of FIG. 4b. For the general case ofUNSYMMETRIC ANISOTROPIC CONICAL boundary conditions, the allowed stateswill not be obtainable by such a simple rotation of a CIRCULAR CONICALboundary constraint surface. Section IX explains that -U-boundaryconditions are required for electric field-induced switching betweenstates of opposite P_(x).

For ANISOTROPIC CONICAL boundary conditions, the surface energy, F_(min)(α), may be different for the various director orientations satisfyingthe constraints. In this case one or several of the allowed orientationsmay be favored over the others.

C. INCOMPLETE CONICAL Boundary Conditions

The intersection of such an INCOMPLETE boundary constraint surface withthe layer constraint cone leads to many of the same geometrical featuresas discussed for the COMPLETE case in the previous section, with onenotable addition. Consider the intersection with the layer cone 112 ofthe boundary constraint surface 110 of FIG. 3e having Ω_(o) ≃90° and itssymmetry axis at an angle Ψ_(o) from z. In this case, only the 5 surfacestate will satisfy the two constraints, making it energetically favoredover the 6 surface state see FIG. 4b and related discussion for surfacestate definitions, which in this case is absolutely unstable (no energyminimum), and making the surface intrinsically monostable. Thus, byoblique SiO evaporation it is possible to favor either the 5 or 6 state.

D. POLAR Boundary Conditions

The following situations produce POLAR orientation: (i) direct couplingto P--for example, a surface covered with discrete dipoles directed awayfrom the surface would tend to align P at the surface in the samedirection, as discussed in Section IV C; (ii) variation of F_(min) (α)withα--with ANISOTROPIC CONICAL boundary conditions, discussed inSections IV A and V B; (iii) absolutely monostable surfaces--obtainedwith INCOMPLETE boundary conditions, discussed in Sections IV B and V C.

FIGS. 6a and 6b indicate the surface orientations adopted with POLARboundary conditions favoring the orientation of P out of and into,respectively, the liquid crystal layer. As with the case of CONICALboundary conditions, externally applied torques may force the surfaceorientation away from this equilibrium condition.

The liquid crystal-surface interaction will, in general, possesscomponents which favor POLAR boundary conditions in addition tocomponents favoring CONICAL. The resulting behavior at the surface willdepend on the relative strengths of the two kinds of interaction. Forexample, if there are only interactions favoring CIRCULAR CONICALboundary conditions, then the four surface states of FIG. 4b(i) will bepossible as to be discussed in Section V. If a weak POLAR surfaceinteraction favoring the orientation of the polarization, P, into thesurface is now added, the result will be an enhancement of the stabilityof the two states of FIG. 4b having P directed toward the surface (1 and2) over the other two. Hence, the addition of the polar interaction willreduce the number of stable states from four to two, although for weakPOLAR interactions the two higher energy states will be me tastable. Inthe two remaining stable, states the angle Ω will be smaller than Ω_(o),as the POLAR interaction will tend to rotate P toward the surface. Asthe POLAR interaction is further increased in strength, P will rotatecloser to being normal to the surface until, at a sufficiently largevalue of the POLAR interaction strength, the polarization willdiscontinuously rotate to be normal to the surface, taking up theorientation of FIG. 6b. In this case, the distinction between states 1and 2 is lost, and the number of stable surface states is reduced toone, 1≡2.

VI. TILTED LAYER GEOMETRY

In the device of said patent the smectic layers were arranged to beperpendicular to the bounding plates (said patent, FIG. 2). The moregeneral situation will now be discussed wherein the bounding plates makesome angle δ with the normal to the layers. In the configuration of FIG.1, bounding surface 102 contains the x axis and is rotated about theaxis by the angle σ from the x axis. The condition δ=0 applies to thedevice of said patent and to discussion of CONICAL and POLAR boundaryconditions up to this point. It is possible to prepare ferroelectricsmectic C layer structures between plane parallel plates in which thelayers are not normal to the plates. In some cases, the surface energywill be significantly lowered by having δ≠0, in which case the layerswill tend to spontaneously tilt from being normal to the surface. Ifthis dependence of surface energy on δ is sufficiently weak, then tiltedlayers can be achieved in several other ways: by displacing, in thesmectic C phase or in the lower temperature range of the smectic Aphase, one bounding plate relative to the other in the direction normalto the layers; by cooling the liquid crystal into the smectic C phase inthe presence of a strong magnetic field; by shear or applied fieldscombined with appropriate boundary conditions. As an example of thelatter, as discussed in Section IV, by slightly oblique evaporation of amaterial like silicon monoxide onto a clean surface, an "INCOMPLETECONICAL" surface orientation results, having, in the simplest case ofΩ_(o) =90°, the director at the surface parallel to the surface and in aparticular orientation. This can lead to a cell having two distinctregions, each with flat smectic C layers, one with the layers inclinedto the surface normal through an angle δ equal to the director tiltangle Ψ_(o), and the other with δ=-Ψ_(o). A further applied field,shear, or surface treatment can then favor one kind of domain over theother, producing a single orientation. This will be discussed further inSection X E.

The major factor governing the layer structure and orientation is thefact that, in a smectic, the layers are difficult to compress. Thus, forstresses usually encountered, taking the layer spacing to be a constantis a very good approximation. As a result, the layer inclination angle,δ, once established, will change little from one area of the sample toanother. In a sample having nearly flat layers, the angle δ will bedetermined by surface interactions, or if these are weak, by occasionalfocal conics or edge dislocations, smectic defects introduced during theprocess of formation of the layers in either the smectic C or A phase,the structure of which is known in the art to establish smectic layerorientation in adjacent volumes. See, for example, M. Kleman, Points.Lignes. Parois, Les Editions de Physique, Orsay, 1978, pp. 165-171, andC. E. Willares and M. Kleman, Le Journal de Physique, Volume 35, pp.L33-37, 1974.

Ferroelectric smectic C structures with tilted layers, when employedwith the boundary conditions discussed above in Section IV, offeradditional advantages in obtaining novel and useful electro-opticeffects. First to be considered is what happens at single surfaceshaving CIRCULAR CONICAL and/or POLAR boundary conditions with aferroelectric smectic C liquid crystal with tilted layers, i.e., δnonzero.

In the general case of CIRCULAR CONICAL boundary conditions and tiltedlayers, the surface orientations are determined by the intersection oftwo cones of constraint 110 and 112 similar to that already discussed inFIG. 4a for δ=0. If δ is increased from zero so as to tilt the lowerpart of the layers up out of the plane of the paper toward the reader,then layer constraint cone 112 will rotate as indicated in FIG. 7a. As aresult, the intersection orientations will rotate as shown there and inFIG. 7b, which indicates layer constraint cone 112 with its axis normalto the plane of the paper as a circle and indicates the intersectionswith surface constraint cone 110 as dots. The sequences (i) to (iv) inFIGS. 7b through 7d give two possible examples of the motion of theintersections as δ is increased from 0. The corresponding motion of theP-n cross-indicated below each step shows the polarization, P, of states1 and 4 rotating so as to become more normal to the surface, P of states2 and 3 rotating to become more parallel to the surface. Note also thatin the two states having P directed toward the top and bottom surfaces,the rotation is counterclockwise and clockwise, respectively. Thissituation will exist with δ in the range Ψ_(o) δ>90°-Ω_(o). For δ=Ψ_(o)+Ω_(o) -90° the intersections giving states 2 and 3 merge so that states2 and 3 become identical, with P parallel to the surface For δ>Ψ_(o)+Ω_(o) -90° states 1 and 4 rotate further and states 2 and 3 remain at270°, according to the discussion of Section V A(iii). The result is asurface orientation having three stable states, 1, 4, and 7. If thelayer tilt is of the opposite sign so as to tilt the lower part of thelayers away from the reader, then the rotations occur with opposite signproducing the states of FIG. 7c and, for δ sufficiently large, the threestates 2, 3, and 8. The orientation of states 1 and 4 for δ>0 (FIGS. 7band 7d) depends on Ψ_(o), Ω_(o), and δ. For Ψ_(o) and Ω_(o) large (Ψ_(o)≃45° and Ω_(o) >70°, FIG. 7b) the orientations of states 1 and 4 willpass through φ=180° and φ-0°, respectively (FIG. 7b, (i) to (iv))producing the states 1, 4 and 7 of FIG. 7b(iv) for sufficiently large δ.Note that in FIG. 7d(iv) states 1 and 4 differ from 7 in sign of P_(x),whereas in FIG. 7b(iv) P_(x) has the same sign in all three states.

VII. INTRINSIC SPLAY OF THE POLARIZATION FIELD

In a bulk ferroelectric smectic there is a spontaneous helicaldistortion of the director and polarization fields in which theazimuthal orientation, φ, increases linearly as a function of distancenormal to the layers (said patent, FIG. 1). This helical twisting of thepolarization field occurs because of a local spontaneous twist and benddistortion of the director field resulting, in turn, from theinteraction of the chirally asymmetric molecules, as discussed by Meyerin Molecular Crystal and Liquid Crystals, Volume 40, pp. 33-48, 1977.Another possible response of φ to this spontaneous twist-bend tendencyis the linear variation of φ as a function of distance parallel to thelayers leading to a splay deformation of the polarization field, ratherthan the twist variation characteristic of the bulk. This distortion isillustrated in FIG. 8a, representing again a cut along a layer plane. Itis not observed in bulk ferroelectric liquid crystals because, in orderto fill space with P having such a distortion, it is necessary tointroduce defects (disclinations) in the orientation field at which φchanges abruptly by up to 180°, as indicated by dashed lines 120 in FIG.8a. The spacing, S, between defects 120 will be governed by the strengthof the local director twist and bend distortions. Such defects arecostly in energy so that the helix, which by virtue of its geometry isdefect free, is the lower energy state in the bulk. In samples of finitethickness such as we are discussing here, however, such defects canoccur at the surfaces and the spontaneous splay of P may, in fact, lowerthe energy of a particular configuration of φ. For example, consider thesituation of FIG. 8b, which shows a ferroelectric smectic 114 betweenidentical, POLAR surfaces 116 and 118 which act to direct P out of thesample. The result is change in φ of ≃180° from one side of the sampleto the other. If the ferroelectric liquid crystal has a spontaneoussplay of P such that the defect spacing, S, is close to the samplethickness, d, then this 180° rotation will naturally occur and thespontaneous splay will tend to stabilize the configuration indicated inFIG. 8b.

As in the case of the bulk ferroelectric helix, the tendency to form aspontaneous polarization splay can be strong (leading to a small S) orweak (leading to a large S) and may be adjusted independently of P, themagnitude of P. For example, a mixture of two materials with the samesign of P but opposite signs of spontaneous splay can have P comparableto the pure materials, but have a much weaker spontaneous splay of P.Whether the spontaneous splay of P is of consequence in a given devicestructure will depend on the size of S relative to the sample thickness,d. If S>>d, then the spontaneous splay should be of little importance.If S≦d, then variations of φ having the spontaneous splay of P will befavored.

VIII. COMBINED FERROELECTRIC AND DIELECTRIC TORQUES IN LIQUID CRYSTALDEVICES

One of the important features of ferro-electricity in liquid crystals,first pointed out by Meyer et al. (op. cit.), is that the bulkferro-electric dipole moment density (p) leads to an electric field (E)induced director torque density, T_(f) (φ)=-PE sin φ for the electricfield direction indicated in FIG. 2, which is linear in E and rotatesthe director to φ=0° for P and E positive. Because the liquid crystalwill also generally possess some dielectric anisotropy, Δε, the directorwill also experience a dielectric torque, T_(d) =-ΔεE² sin 2φ,well-known in the art to produce molecular reorientation as, forexample, in twisted nematic devices. For positive Δε the torque T_(d)orients the director to either φ=90° or 270°. It is possible to makeferroelectric liquid crystal structures where the presence of bothtorques leads to novel electro-optic effects.

For E small T_(f) dominates since it is linear in E and T_(d) varies asE². The two torques can be comparable for a "crossover field", E_(f-d)≈P/Δε. For E>P/Δε, the dielectric torques dominate. For Ae positive,reorientation from φ=0° to φ=90° or 270° can be achieved by increasingthe field. This reorientation will occur as a Freederikz-liketransition, i.e. there will be no reorientation until the thresholdfield, E_(th), given by the equation, Δε(E_(th))² -PE_(th) =K(π/d)², isreached, beyond which φ will change continuously from 0°. For typicalmaterials, like DOBAMBC and HOBACPC discusssed in the originalapplication, E_(f-d) ≈10⁵ Volts/cm. In Section IX G examples of devicesemploying both ferroelectric and dielectric torques will be presented.

IX. DEVICE STRUCTURES AND DEVICE STATES

A. Introduction

This application deals with Surface Stabilized Ferroelectric LiquidCrystal device structures of the type described in said patent anddepicted therein in FIG. 1, having a ferroelectric liquid crystalbetween the plates of an optically transparent parallel plate capacitorin which an electric field can be applied normal to the plates. Usingthe generalized boundary conditions, layer tilt, and intrinsicpolarization splay described above in various combinations, makespossible a wide variety of configurations of the orientation field, φ,and associated novel electro-optic effects. The devices to be describedall have the important feature in common with the basic device of saidpatent, that: (1) the layers are planar and normal to a specifieddirection over the entire sample; and (2) the liquid crystal layer issufficiently thin that surface interactions stably unwind the intrinsichelix. These conditions result in a basic advantage in electro-opticapplications, namely that the response time for electric field-inducedmolecular reorientation is minimized, being determined by intrinsicoften rational viscosity, and not by the field-induced elimination oflong-lined topological defects. We describe devices having single andmultiple (up to 16) electrically accessible stable states. It ispossible to surface-stabilize up to 4 states at each surface, hence atotal of 4×4=16 device states is intrinsically possible in the generalcase.

Employing these generalized surface, intrinsic splay, and layer tiltconditions will clearly lead to many possible device structures withrather diverse molecular orientation states and switching properties. Asa result, it has been necessary to develop a classification scheme aboutwhich the discussion of these properties will be organized. A device ina given orientational state will be named according to its DEVICESTRUCTURE and particular overall orientational DEVICE STATE as follows:

DEVICE STRUCTURE:DEVICE STATE

The DEVICE STRUCTURES are classified according to whether the layers arenormal (N) or tilted (T) and as to the nature of the surface conditionsemployed: CIRCULAR CONICAL (C), SYMMETRIC ANISOTROPIC CONICAL (S),UNSYMMETRIC ANISOTROPIC CONICAL (U), and/or POLAR (P). If thespontaneous splay of P is important for the working of the device, thedesignation (Y) will be added. Each DEVICE STRUCTURE is assigned analphanumeric code as follows: ##STR1## For CIRCULAR CONICAL boundaryconditions a numerical superscript will indicate the cone angle Ω_(o),if it is to be specified, e.g. C⁹⁰ implies Ω_(o) =90°. A STRUCTUREhaving identical boundary conditions on the two surfaces will beindicated by a single boundary condition specification "squared", forexample, the boundary condition of the device in said patent is (C⁹⁰)².If a STRUCTURE has boundary conditions of the same class but withdifferent parameters on the two surfaces, this will be indicated bydifferent subscripts, e g C₁ C₂. The terms "top", "bottom", "UP", and"DOWN" are employed merely as descriptive, the actual direction of thegravitational acceleration being of no relevance to the operation ofthese devices. As an example of this classification scheme the DEVICESTRUCTURE of said patent is:

    N-(C.sup.90).sup.2.

A given DEVICE STRUCTURE can have many possible overall orientationalDEVICE STATES since there are a variety of stable STATES possible ateach surface. Many of these DEVICE STATES can be characterized by givingthe single states (numbers 1 to 8 of FIGS. 4b and 5) at the twosurfaces. These numbers designate either the single surface statesobtained with CIRCULAR CONICAL boundary conditions (FIG. 4b) or thesingle surface states which evolve from those of FIG. 4b when surfaceconditions become unsymmetric (FIG. 5) or the layers are tilted (FIGS.7b, 7c and 7d). Our convention will be to express the overall DEVICESTATE by a colon followed by the top surface state and then by thebottom surface state. Although the numerical single surface statedesignation 1 to 8 of FIGS. 4b and 5 are defined relative to the topsurface (and the x,y,z system), they will also be applied to the bottomsurface in the way that states having the same orientations in space atthe top and bottom surfaces have the same designations. With thisconvention DEVICE STATES having repeated single surface states, i.e.:55, will have the same or nearly the same orientation of the directorin space at both surfaces (like corresponding orientations in FIG. 4band c). Using this notation, the two allowed DEVICE STATES of the DEVICESTRUCTURE in said patent are:

    N-(C.sup.90).sup.2 :55 and N-(C.sup.90).sup.2 :66.

Thus, the DEVICE STRUCTURE, N-(C⁹⁰)², has two DEVICE STATES, :55 and:66.

In the next sections, examples of DEVICE STRUCTURES and DEVICE STATESwill be discussed, considering, for a particular DEVICE STRUCTURE,electric field-induced transitions between different DEVICE STATES andfield-induced modification of DEVICE STATES. To facilitate thisdiscussion, we establish the convention indicated in FIG. 9a forelectric field direction, an UP (+) field being directed toward the TOPplate and vice versa.

With the exception of the N-(C⁹⁰)² :55 STATE having φ=180° everywhere,the application of an UP field to a DEVICE STATE will change the spatialdistribution of φ(x,y,z) between the plates from that determined solelyby the boundary conditions and bulk elasticity, generally rotating Pinto the direction of E. This field-induced reorientation will, ingeneral, alter both the surface orientations and the torque per unitarea exerted by the liquid crystal on the surfaces. At low fields, theresponse will be a continuous rotation of the director from itsfield-free value. As the electric field is increased, however, theoverall bulk plus surface energy, U, may be reduced by the change ofsurface state, with a rotation of P toward E reducing electrostaticenergy and director elastic distortion energy, with either a decrease orincrease of surface energy. Such a process may be continuous ordiscontinuous, in the latter case occurring by the motion of discretedomain boundaries which separate the two states. Stated another way,once the field is applied, a given surface-stabilized state representsone of several local minima in U vs φ_(t) and φ_(b), the orientation atthe top and bottom surfaces respectively. These minima are separated bymaxima, which can be considered to limit the orientation range of agiven surface state. The system will, in general, adopt the state havingthe lowest minimum in U. Changes of state can thus occur in the twofollowing ways. As the field increases, one state may decrease in energyat a faster rate than others, becoming, at some critical field, thelowest energy state. In this case, the surface state change would bediscontinuous, occurring by domain wall motion (i.e. would be"first-order", in analogy with discontinuous bulk phase transitions).Alternatively, as the field increases, a local minimum in U maycontinuously move toward, and meld with an adjacent minimum, resultingin a continuous, ("second order") change of surface state.

Depending on the particular case, there can be several such changes ateach surface in a STRUCTURE, leading to many possible field-inducedchanges of DEVICE STATE. On the other hand, application and removal of asufficiently low field may not result in the change of STATE, but onlythe modification of the STATE while the field is on. In general, thefield-induced variations in φ (x,y,z) may be classified as follows:

(i) NO STATE CHANGE (NO)--φ(x,y,z) varies continuously with increasingfield, with U vs φ_(t) and φ_(b) remaining in the same local minimum.For examples, see Section IX F.

(ii) FIELD-INDUCED STATE CHANGE (FI)--As E increases from zero, φ variescontinuously until, at some critical field, there is a surface statechange. When the field is reduced, this surface state change reverses,leaving the original STATE when the field is removed. For examples, seeSection IX F.

(iii) PERMANENT STATE CHANGE (PERM)--As E increases from zero, φ variescontinuously until, at some critical field, there is a surface statechange. When the field is reduced, this surface state change iscompleted, leaving a new STATE. For examples, see Sections IX B and C.

In the Sections that follow, PERM changes are primarily indicated anddiscussed, showing schematically the n-P configuration before and aftera field pulse of finite duration. For a sufficiently small field or forsufficiently large surface energies, each of the PERM change and FIchange processes will reduce to a NO change process. Such an example isindicated in Section IX F. Alternatively, processes are possible whichare successively NO, FI and, PERM with increasing field. Section IX Bgives an example. We now discuss particular cases.

Persons skilled in the art would recognize that devices employing theeffects described in subparagraphs (ii) and (iii) above are, by virtueof their state changes, intrisically non-linear.

B. Devices Employing CIRCULAR CONICAL (C--C) Boundary Conditions

1. N-C² STRUCTURES

FIGS. 9a-9c show examples of stable DEVICE STATES obtained with δ=0, nointrinsic splay, and identical CIRCULAR CONICAL boundary conditions onboth surfaces (N-C²). The special case of the device of said patent,N-(C⁹⁰)², is shown in FIG. 9a for two of its stable STATES :55 and :66.The horizontal arrows between the STATES indicate transitions induced byfinite duration electric field pulses of the direction and magnitude ofthe accompanying vector. The general case, which is shown in FIG. 9bhas, with the same orientations on the two surfaces caused by aligningmeans 116 and 118, four stable DEVICE STATES, N-C² :11, :22; :33, and:44 for liquid crystal 114. Application of electric field pulses createdby electrodes 122 with the electric field directed upward (UP field)will induce switching from STATE :44 to :11 or :33 to :22; a DOWN fieldwill switch from STATE :11 to :44 or :22 to :33. Note that since thefield induced torques will rotate STATE :11 clockwise, the next stableSTATE encountered will be :44. Once the system is in :44, a largerelectric field applied in the same direction will tend to rotate :44further clockwise, with the angle φ going to zero for sufficiently largefield. When the field is removed the system can return either to the :44or :33 STATE, depending on random fluctuations. Thus, STATES :22 and :33will not be reliably accessible if the system is initially prepared inSTATES :11 or :44. Similarly, :11 and :44 cannot be reliably reachedfrom :22 or :33. Hence, the field must be kept sufficiently low tomaintain the system in either the :11,:44 or :22,:33 pairs of STATES. Ineither case, what would result is bistable switching similar incharacter to that of said patent but with two useful differences: i)upon switching, the reorientation, 2Δ.sub.χ, of the projection of theoptic axis direction (also given by n) on the surface plane will not be2Δ.sub.χ 2Ψ_(o), as in said patent, but will be 2Δ.sub.χ =2 sin⁻¹ {sinΨ_(o) cos[sin⁻¹ (cos Ω_(o) /sin Ψ_(o))]}, which in general will be lessthan 2Ψ_(o). Thus, the optical properties will depend on both Ψ_(o) andΩ_(o), giving more flexibility in the manipulation of the opticalproperties, for example: (i) choosing boundary conditions with Ω_(o)increasing with increasing temperature could reduce the effects of Ω_(o)decreasing with increasing temperature; (ii) once switched into any ofthe four STATES, further increase in the electric field will produce nofurther STATE change, but will increase Δ.sub.χ, the angle between theoptic axis and layer normal projections onto the surface plane. Thiscontinuous reorientation of the optic axis about a stable STATE producesa birefringent phase shift that can be continuously varied (TUNABLEBIREFRINGENCE). The accompanying changes in optical transmission wouldbe useful in some applications, for example it would be a way ofachieving a partial grey scale in video applications.

In some applications the existence of two independent sets of STATES,(:11,:44) and (:22,:33), could itself be useful. For example, with lightincident obliquely to the surface plane, the four STATES will in generalexhibit varying amounts of relative phase shift for ordinary andextraordinary polarization and thereby can exhibit differentbirefringence colors. Hence, an array of :11,:44 areas might performswitching between two colors, while adjacent :22,:33 areas performswitching between a different set of colors. Initial selection of eitherthe (:11,:44) or (:22,:33) STATES could be made by an electric fieldapplied parallel to the bounding plates, by appropriately employing thesame electrodes that are used for switching.

For the surface tilt angle, Ω_(o), small, and CIRCULAR CONICAL boundaryconditions, the stable surface states are states 7 and 8 of FIG. 4b. Adevice with two such identical surfaces will yield configurations :77and :88 of FIG. 9c. For low electric field values, either of thesestructures will yield a continuous variation with E of the averageorientation in the liquid crystal layer, φ_(ave), which is linear aboutthe equilibrium φ (90° for 8 and 270° for 7). The linear Variation ofφ_(ave) will lead to a linear variation in the sample birefrigence. SuchDEVICE STRUCTURES should thus be of particular use in obtaining highspeed linear liquid crystal electro-optic devices. In addition, forsuitably dichroic molecules, a quadratic variation of sample opticalabsorbance with E can be obtained. Following the arguments of theprevious section, it should not be possible to reliably switch betweenthe two STATES (:77)⃡(:88) with an E field applied normal to the plates.

2. N-C₁ C₂ STRUCTURES

If the boundary conditions are CIRCULAR CONICAL, but with different coneangles, Ω_(o), or different surface energy anisotropy, Γ, on the twosurfaces, then the N-C₁ C₂ STRUCTURES result, examples of which areshown in FIGS. 10a and 10b. Having surfaces of different characteristicsleads to an important new qualitative feature of the response of thesystem to applied electric fields, namely that the surfaces can beswitched independently, leading to a larger number of DEVICE STATES thatcan be induced by electric field pulses. FIG. 10a shows a C₁ C₂STRUCTURE with molecules of liquid crystal 114 having different surfacetilt angles at aligning means 116 and 118. The application of a DOWNfield pulse by electrodes 122 to the :11 STATE will induce switching atthe top surface at smaller fields than for the bottom, leading, for somevoltage range, to switching to the :41 STATE. A larger DOWN pulse willswitch the bottom surface, producing the :44 STATE. Comparing to FIG.9b, we see that the mixed boundary conditions lead to the possibility ofhaving an extra device STATE with mixed surface states. This thirdDEVICE STATE has a highly nonuniform director orientation and willexhibit birefringence and optical rotation effects which are distinctlydifferent from the :11 and :44 STATES. In conjunction with crossedpolarizer and analyzer, this DEVICE STRUCTURE could produce oneextinguishing and two colored DEVICE STATES, or could behave as a threecolor switch. FIG. 10b shows the case with a small Ω_(o) on one surfaceat which the orientation is either 7 or 8. Applied fields can switch theopposite surface, producing either of the two state devices indicated.

Note a feature common to the :41, :32, :18, and :27 STATES, which alsoappears in many of the STATES to be described, namely that the directorprojection onto the surface plane rotates monotonically as one proceedsfrom one side of the sample to the other. These are called TWISTEDSMECTIC STATES, in analogy with the similar director rotation in"twisted nematic" devices. The optical properties of these STATES arediscussed later in Section IX F, in connection with the TWISTED SMECTICSTATE of FIG. 8b.

C. Devices Employing UNSYMMETRIC ANISOTROPIC CONICAL (U-U) BoundaryConditions

1. N-U² STRUCTURES

A striking feature of the devices employing CIRCULAR CONICAL boundaryconditions, illustrated in FIGS. 9a-9c, 10a and 10b, is that, with theexception of STATES :55 and :66 which have P vertical, these STRUCTUREScan be divided into two groups, one with the horizontal component of P,P_(x), to the right, the other with P_(x) directed toward the left.Switching between these groups is not possible with CIRCULAR CONICAL orSYMMETRIC CONICAL boundary conditions (discussed below). However, withUNSYMMETRIC ANISOTROPIC CONICAL (U) boundary conditions, left-rightswitching becomes possible, allowing a variety of new devices similar tothose of FIGS. 9a-9c, 10a and 10b, but wherein all of the STATES in agiven device are electrically accessible.

If TILTED boundary conditions with Ω small are used, the N-U²orientation configurations relative to aligning means 116 and 118 becomethose of FIG. 11a, showing the clockwise φ reorientation of both statesrelative to the CIRCULAR CONICAL case (FIG. 9c). In addition, thesurface energy maximum which occurs as φ is increased from :88 to :77,also rotates from being at φ=180° as in FIG. 9c to some φ<180° in FIG.11a. As a result, application of a sufficiently strong UP field withelectrodes 122 to :88 can turn φ past this energy maximum such that whenthe field is released φ will rotate to :77. Once in :77, a sufficientlylarge electric field pulse of the opposite polarity will switch thedevice back to the :88 by the same reasoning. This switching willproduce a reorientation of the effective optic axis for light incidentnormal or nearly normal to the surface plane that is similar to, butsmaller than, that of the device of the original application. Such asmall optic axis rotation can be exploited in (simpler to fabricate)large thickness devices (i.e. d>10 μm) , made with long pitchferroelectric liquid crystals. Liquid crystals of long pitch may becreated by mixing non-chiral liquid crystal material with chiralmaterials, or by mixing chiral left and chiral right liquid crystalmaterials so as to produce a net, slight chiral effect. In addition, the:77 to :88 switching will exhibit a large optic axis reorientation forlight incident obliquely and normal to the director, but very littleoptic axis reorientation for light incident in the plane containing thedirector. Hence, selection of obliquely incident light is possible.

By employing UNSYMMETRIC ANISOTROPIC CONICAL boundary conditions withΩ_(o) large (>70°) it is possible to make a device wherein any of thefour STATES, :11, :22, :33, or :44 is obtainable by application ofelectric field pulses. We consider a DEVICE STRUCTURE with a substantialdirector tilt angle Ψ_(o) ≈45° and UNSYMMETRIC ANISOTROPIC CONICALboundary conditions modeled by the titled cone of FIG. 3c with a largesurface tilt angle, Ω_(o) ≈70° and a small cone axis tilt of β≈15°parallel to the layer planes (γ≈0). For these conditions there will befour stable STATES, as indicated schematically in FIG. 11b. ComparingFIG. 11b to FIG. 9b, we note that the effect of the surface cone tilt isto rotate clockwise the orientations of all of the STATES. The surfaceenergy maxima between the STATES are also rotated. As a result,application of a sufficiently strong UP field by electrodes 122 to :11can turn φ past this energy maximum such that when the field is releasedφ will rotate to :22. Once in :22 a moderate DOWN pulse can take thesystem to :33 as discussed in connection with FIG. 9b. A larger oppositepolarity pulse will take :33 to :44, just as discussed for :11 to :22.Switching from :44 to :11 proceeds as for :22 to :33. Hence, with pulseshaving appropriate peak voltages V₁ >V₂, the sequence V₁, V₂, -V₁, -V₂,. . . will continuously decrease φ, taking the system around the loop:11, :22, :33, :44, . . . . The orientation may be stopped in any one ofthese STATES by appropriately stopping the pulse sequence. In a devicehaving the surface constraint cone tilted in the opposite direction, theopposite sense of rotation will be produced for the same pulse sequence.

Related devices can be made with relatively strong, well known, boundaryconditions on one surface, fixing this surface permanently in any of thestates 1 to 8 for a field strength that will switch the other surfaceamong states 1 to 4 as described in the previous paragraph.

These various DEVICE STATES can be exploited in conjunction with crossedpolarizers to produce birefringence based between four distinct colors,or between three colors and an extinguishing state.

2. N-U₁ U₂ STRUCTURES

As with the CIRCULAR CONICAL boundary conditions, relaxing the conditionthat the two surfaces be identical leads to a larger number ofelectrically accessible STATES in U-U STRUCTURES. FIG. 12a shows a fourSTATE N-U₁ U₂ STRUCTURE with STATES 5 or 6 at the two surfaces, leadingto four possible configurations, :55, :65, :66, and :56. If the surfaceanchoring is weaker or the tilt angle larger at the top surface, thenthe sequence of these STATES obtained is shown in FIG. 12a. A weak DOWNpulse will switch :55 to :65. A stronger DOWN pulse will switch thebottom, producing :66, and the same sequence with UP pulses willcomplete the remaining two steps of the cycle.

FIG. 12b shows half of the DEVICE STATES achievable with a U₁ U₂STRUCTURE having STATES 1,2,3, or 4 on the two surfaces. This STRUCTUREhas in principle 4² or 16 possible overall STATES and for judiciouschoice of parameters all can be electrically accessed. The figure showshalf of the switching cycle for the case having weaker surfaceconditions on the top surface. None of these STATES have identicalmolecular or molecular orientation configurations, hence they may bedistinguished optically, either by their birefringence or dichroism orboth. With appropriate choice of parameters, such a multistate devicecould be used to produce color or gray-scale effects.

In a U₁ U₂ device, the relative direction of the anisotropy on the twosurfaces is another variable of interest. For example, with the-U-boundary condition given by the tilted cone of FIG. 3c, the sign of βon the bottom surface can be the same or opposite to that on the top.The sign is the same for the device of FIG. 12a. FIGS. 13a and 13billustrate the opposite choice wherein the anisotropy introduced byaligning means 116 and 118 are in opposite directions, FIG. 13a showing:11 to :14 switching, and 13b a novel bistable switching sequence, shownstarting with :21. A DOWN pulse created with electrodes 122 applied to:21 gives the indicated :43 STATE which has a rotation of P of ≃360°from top to bottom, in contrast to the :44 STATE of FIG. 10b. Thisstate, however, is inherently unstable against a bulkdisclination-mediated transition to the :43 state shown to the right inthe FIGURE, and thus could only be used as a transient state. Thisexample shows that the surface state designation does not uniquelycharacterize a device state.

D. Devices Employing Mixed CIRCULAR CONICAL and UNSYMMETRIC ANISOTROPICCONICAL (C-U) Boundary Conditions

FIGS. 14a and 14b show examples of devices with C-U boundary conditions.Having unsymmetric anisotropic tilt at just one surface is sufficient toallow the left-right switching of P found in the U-U devices. One suchprocess is illustrated in FIG. 14a which starts with the N-C-U:88 STATE,with aligning means 116 providing CIRCULAR CONICAL boundary conditionsand aligning means 118 providing UNSYMMETRIC ANISOTROPIC boundaryconditions. With an UP field applied, molecules near bottom surface 118can be rotated to the 7 state in analogy with the process of FIG. 11aleaving an :87 overall STATE. In this STATE, the overall elastic plussurface energy will exhibit a maximum for φ_(t) <180°, where φ_(t) isthe orientation of molecules at top surface 116, as φ_(t) is increasedthrough 180°. Note that the top surface energy alone is maximum at φ_(t)=180° but, because the elastic distortion in the :87 STATE favorsincreasing φ_(t), the overall energy will be lowered by increasingφ_(t). If an UP field which is large enough to rotate φ_(t) through thismaximum is now applied and removed, the orientation of molecules at topsurface 116 will relax to the 7 state, leaving a :77 overall STATE. ADOWN pulse will now switch molecules near bottom surface 118 to STATE 8,leaving :78, from which a larger DOWN pulse can switch molecules neartop surface 116 back to 8 via the mechanism just described. Thus, a FOURSTATE device is possible.

FIG. 14b shows a N-C-U STRUCTURE with STATES 1, 2, 3, or 4 on the topsurface and 7 or 8 on the bottom. All possible combinations of thesesingle surface states are electrically accessible, making this an EIGHTSTATE device. The switching mechanisms involved have all been discussedpreviously, with the 7-8 switching near bottom surface 118 beinganalogous to the switching in FIG. 11a, and the 1-4 switching near topsurface 116 being like that of the top. surface switching in FIG. 14a.

E. Devices Employing Tilted Layers (T)

FIGS. 15a-15d show several examples of the possible STRUCTURES havingtilted smectic layers for which the single surface states are those ofFIGS. 7a-7d. FIG. 15a shows the DEVICE STATES achievable with identicalsingle surface states 1, 2, 3, and 4, and the layer tilt conditions ofFIG. 7b(ii), wherein states 1 and 4 have rotated through the horizontal.This T-C² STRUCTURE has four stable STATES all having the horizontalcomponent of P to the left. Any of these states can be switched to anyother, with the :22 (:33) being obtained for moderate UP (DOWN) pulsesand the :11 (:44) obtained for large UP (DOWN) pulses.

As for the devices of FIGS. 9a-9c, the boundary conditions can begeneralized to C₁ C₂, producing additional field accessible states. Ifthe bottom surface near aligning means 118 has the larger surface energyanisotropy (is the stronger) then the sequence of FIG. 15b, showingeight of sixteen pulse switchable states, is possible. The switchingfrom :41 to :42 in FIG. 15b indicates how elasticity in the bulk can actto favor particular response to applied field. In generating the :41STATE a strong orientation gradient is introduced into the sample. Thisgradient applies torques to the surfaces tending to force rotations thatwill unwind the bulk. Application of an UP pulse acts on the top surfaceto wind the bulk tighter but acts on the bottom to unwind it. The resultis that the field, acting in consort with the bulk elasticity, reorientsthe bottom surface to reduce the bulk gradient. Hence, in a givensituation, the bulk configuration of φ can influence the switchingsequence.

If the single surface states are those of FIG. 7b(iv), i.e. states 1, 4,and 7 with P to the left, then devices with an odd number of stableSTATES can be made, as indicated in FIGS. 15c and 15d. In FIG. 15d, thebottom surface near aligning means 118 is stronger.

F. Devices Employing POLAR (P) Boundary Conditions

A POLAR term in the boundary condition can be added to any of the aboveSTRUCTURES and will tend to stabilize those STATES having, at thesurface, the preferred direction of P relative to the surface normal.For example, in FIG. 10a, a POLAR interaction forcing P to be directedin from bounding planes 116 and 118 will stabilize STATES :41 and :32relative to the others. Hence, the POLAR interaction may be used toadjust and balance the relative stability of various STATES. StrongPOLAR interactions will stabilize the STRUCTURE N-P² :56 of FIG. 8b,producing a single STATE STRUCTURE which has useful electro-opticproperties. In the zero field state, which is TWISTED SMECTIC (cf.Section IX B 2), the director, when projected onto the surface plane,makes a rotation of 2 Ψ_(o) as one proceeds from one side of the liquidcrystal layer near plane 116 to the other near plane 118. This "twist"of the director projection is similar to that found in many other of ourdevices (cf. FIGS. 10a-13b) and is similar to that introduced intotwisted nematic cells. It is well known in the art to produce a simplerotation of the plane of polarization of light, if the distance overwhich significant rotation occurs is long compared to the wavelength ofthe light (Mauguin limit). In the case of very thin cells (d≈ severalμm) this condition is only roughly satisfied but the polarizationrotation is still generally observed, with the exiting light beingslightly elliptically polarized. Application of an UP or DOWN field willrotate the polarization in FIG. 8b to the :55 or :66 STATE,respectively, with the field on, the STRUCTURE being a uniform uniaxialslab with different orientations in the two cases. These three STATESthus offer quite distinct optical properties. The response of the :56STATE about the equilibrium STRUCTURE is linear for small fields, sothat this STRUCTURE can give high speed linear electro-optic effects.

G. Devices Employing Combinations of Ferroelectric and DielectricTorques

As an example of a device employing both ferroelectric and dielectrictorques, consider FIG. 9b which can be ferroelectrically switchedbetween the :11 and :44 STATES. For fields larger than the crossoverfield the dielectric torques will dominate and the director willreorient, :11 to :88 and :44 to :88. Thus, as a result of the dielectrictorques, one additional field-induced STATE is available. An additionaleffect of the dielectric torques will be the field induced tilt of thelayers. Once STATE :88 is obtained the director, the axis of largest ε,makes an angle 90°-Ψ_(o) with the electric field, implying a fieldinduced torque parallel to the layer planes. This torque will act torotate the layers which, in turn, will vary the sample birefringence,producing in this case a quadratic electro-optic effect. Dielectrictorques may also be used to enhance the switching speed by increasingthe electric field amplitude when the orientation φ is such thatdielectric torques couple more strongly to the field than ferroelectrictorques (e.g. for φ≈45°).

H. Device Variations

1. Boundary and Layer Tilt Conditions Approximating Those of U.S. Pat.No. 4,367,924

In said patent the boundary and layer tilt conditions were respectivelyΩ_(o) =90° and δ=0°. Some preparation techniques will closelyapproximate these conditions while not satisfying them exactly. Forexample, aligning the layers with a magnetic field which is notprecisely parallel to the surface planes will produce a structure havingδ≈0°. Alternatively, some surface treatments might produce an Ω_(o)close to, but slightly less than 90° or there may be a slight POLARcontribution to the boundary condition. In any of these cases, theoperation of the device will be essentially the same as in said patent.That is, the conditions Ω_(o) =90° and δ=0° need not be exactlysatisfied for a device to operate essentially as in said patent,switching between :55 and :66 states. The range of deviation from theoriginal values of the angles Ω_(o) and δ over which operation as theoriginal device will obtain will depend on the particular situation, butdeviations of less than 5° should in most cases yield devices operatingessentially as in said patent.

2. Devices with Pretilt

An additional possible use of TILTED boundary conditions as in theSTRUCTURE of FIG. 9b is the establishment of pretilt. Considering FIG.9a, the application of a DOWN field to :55 will induce switching to :66.However the switching could proceed by either clockwise (φ decreasing)or counterclockwise (φ increasing) rotation. Adjacent regions switchingin these opposite reorientations would end up separated by a 360°disclination wall in the φ field once the switching was completed. Thepresence of such walls, which may have to travel long distances tocoalesce and anneal away, will generally slow the completion of theswitching process. Pretilting the director with TILTED boundaryconditions, such as for the :11 state of FIG. 9b, forces thereorientations to go in one of the directions (clockwise for the :11state), thereby eliminating the disclination walls and speedingswitching.

3. Devices with Nonhomogeneous Bounding Plates

Up to now DEVICE STRUCTURES have been described which are homogeneous inthe sense that the surface treatment and liquid crystal layer thicknessare the same everywhere on the bounding plates. Device variations withnovel properties can be made by relaxing either or both of thesehomogeneity conditions.

Consider first a device having a liquid crystal layer thickness which isvariable, having, for example, one of either two thicknesses. Means foraccomplishing this are discussed in Section X B. Altering the liquidcrystal layer thickness affects both its optical properties and thecharacteristics of its response to electric field. For example, in anyof the devices having uniform director orientation (c.f., FIGS. 9a-9c),disposition of the liquid crystal layer between crossed polarizers withwhite light incident, yields transmitted light, the color of whichdepends on the thickness according to the well known birefringence colorsequence. Hence, different colors of light can be produced by differentparts of the liquid crystal layer, as determined by the local layerthickness. Devices employing this technique to generate color arediscussed in Section X B.

On the other hand, changing the thickness can strongly affect theswitching characteristics, changing the electric field in the liquidcrystal for a given applied voltage, and changing the energies anddissipation of the molecular reorientation. For example, consider thatPOLAR surface interactions stabilize a 180° rotation of P across thesample in the :56 DEVICE STATE of FIG. 8b. If the sample thickness isreduced, increasing torque is required at the surface to maintain thestate. Eventually, at sufficiently small layer thickness, the maximumsurface torque will be reached and the state will unwind into the :55 or:66 STATE, becoming uniform. As this critical layer thickness isapproached, the electric field required to unwind the 180° rotation willdecrease, lowering the voltage required for a state change.

Alternatively, the required voltage can be lowered by weakening thePOLAR surface interaction strength, so that, in a structure with anonhomogeneous surface treatment yielding weaker POLAR interactions insome regions, these regions will switch (unwind) first as the appliedelectric field is increased, and return to the :56 state last as E isdecreased. This nonhomogeneity can be different on the top and bottomplate, such that one region has a weaker top surface and therefore alower voltage threshold for the field-induced :56→:66 transition thanfor the :56→:66, and, in another place, a weaker bottom surface and theopposite threshold behavior. It is evident that, by varying theconditions over the bounding surface, a given single structure canlocally exhibit many of the field-induced reorientations described inFIGS. 8a through 15d. Application of these ideas in device switching isdiscussed in Section X E.

Nonhomogeneous surface treatment may also usefully serve as a tool forobtaining uniform alignment of the smectic layers, as will be discussedin Section X E.

Finally, in addition to surface treatment and sample thickness, thelayer tilt may be varied nonhomogeneously, producing the variabilitydiscussed above for tilted layers in attainable local STATES.

4. Devices Employing Temperature as a Variable Parameter

We consider here devices in which heat pulses are applied to the liquidcrystal layer, either electrically or optically, while in a given DEVICESTATE or during a STATE change.

Such a temperature variation can alter the optical properties of aDEVICE STATE, primarily by changing the smectic tilt angle, Ψ_(o),giving a single electrically addressed STATE the possibility ofexhibiting several, or a continuum of optical transmissivities orcolors. Specific effects are discussed in Section X D.

Alternatively, heat pulses can be used alone or in conjunction withfield pulses to switch between DEVICE STATES. Consider, for example, thedevice of said patent employing a material such as DOBAMBC in theferroelectric smectic F phase. Employing the F phase has the advantagethat it exhibits very strong bistability, but the disadvantage of veryhigh viscosity and consequent slow switching. This latter difficulty canbe overcome by heating the material into the smectic C phase during theswitching pulse, making use of its much lower viscosity and fasterswitching. Calculations of thermal response are available in the art (D.Armitage, Journal of Applied Physics, Volume 52, pp. 1294-1300, 1981),and indicate that a 1 micron thick liquid crystal layer could be heated≃20° C. and cool within ≃10 microseconds. On the other hand, a heatpulse alone, taking the smectic up to the A phase, could be used toswitch a metastable STATE (e.g. :65 of FIG. 12a) to one of lower energy(:55 of FIG. 12a).

X. EXAMPLES OF SSFLC DEVICES

A. Introduction

The fast electro-optic switching of the SSFLC geometry has devicepotential in several areas of electro-optics. Flat panel SSFLC displayscan be made active (with built-in light source and working intransmission) or passive (using ambient light to work in a reflective orabsorptive mode) with applications to instruments and gauges,oscilloscope and radar screens, screens for computer and word processingsystems, monochrome or color television, etc. Other applications includeany of those where the twisted nematic has been demonstrated orproposed, but higher response speed is needed, such as fiber-opticswitches, optical and acoustical detectors, and incoherent-coherenttransducers. To cite a further example, SSFLC switching promises toeliminate the major stumbling block of parallel opticalprocessing,namely the slow speed of available light valve arrays. Inthis section, we discuss some specific applications of the variousDEVICE STRUCTURES and DEVICE STATES of this application and said patent.

B. Applications of Devices Employing Two-State Pixels

Here applications of SSFLC devices are discussed employing pixels whichexhibit two optically distinct DEVICE STATES. These two states maydiffer by either temporary or permanent field-induced change of bulk orsurface orientation. These distinct possibilities were detailed inSection IX A.

The term PIXEL means any contiguous discrete electrode area over which auniform electric field can be applied to the liquid crystal. Examples ofelectrodes employed in the art include patterned conductive layers(aluminum, indium tin oxide, etc. ), and active semiconductor elementssuch as thin film transistors, photodiodes, or photoconductors.

The term OPTICALLY DISTINCT in connection with device states means thateither the transmissivity or reflectivity of a combination of the liquidcrystal layer with polarizers, birefringent plates, and/or dichroic dyeschanges upon switching from one state to the other. These changes, ΔTand ΔR, respectively, will, in general, depend on the wavelength oflight employed.

With monochromatic light incident, two-state pixels can be used toswitch between two intensities. With white light incident, because ofthe wavelength dependence of ΔT and ΔR, two-state pixels can switchbetween two colors. Special cases of two-color devices are: 1) black andcolor or black and white devices, distinguished by one state which isextinguishing or nearly so; and 2) color and white devices.

1. Device in U.S. Pat. No. 4,367,924

The original application describes the first kind of device, switchingin transmission between an extinction state and a color/white stateusing two crossed polarizers and the liquid crystal birefrigence. Theapplication also points out that the device will operate in a reflectivemode. The color is a birefringence color determined by the combinationof liquid crystal material and layer thickness, and polarizer setting.Apart from the initial prototypes, devices of this kind have been madeand are illustrated in N. A. Clark, M. A. Handschy, and S. T. Lagerwall,Molecular Crystals and Liquid Crystals, Volume 94, pp. 213-234, 1983.

With crossed polarizers, excellent extinction can always be achievedwith one of the polarizers parallel to one of the director states, e.g.:55 in FIG. 9a. Thus, as illustrated in FIG. 16, liquid crystal 114 issandwiched between aligning means 116 and 118 which creates state :55 or:66. Polarizers 129 and 131 have polarization directions perpendicularlyoriented. State :66 is enterable by applying a voltage across sampleelectrodes 130 and 132, can then be made to produce the colors in thewell known birefringence color sequence at the liquid crystal layerthickness indicated: first order white (≈0.5 μm), yellow (≈1.0 μm),purple (≈2 μm); second order blue (>2 μm), yellow, red; third ordergreen, etc. The indicated layer thickness figures are approximate,depending on the liquid crystal optical anisotropy and tilt angle, and,thereby, on the temperature for many substances. The second order colorsare less sensitive to changes in these parameters than the first ordercolors.

2. Non-Emissive Screens

The ergonomic problems connected with the use of available CRT terminalshave prompted search for ways of developing NON-EMISSIVE screens,alternatively called passive screens. These have to work in reflectionand the principal constituent of the screen has to be rapid because, ingeneral, many elements have to be addressed for every frame updating. Itis clear that the SSFLC structure here offers one of the most attractivesolutions. Although the principles are already contained and mentionedin the original application, and thus nothing basically new can be addedhere in this paragraph, we nevertheless want to give some concreteexamples, in order to illustrate how the practical design and theproperties of the screen may vary.

A reflective device, as illustrated in FIG. 17, using just one polarizer136--in the front--is optically equivalent to a transmissive device withtwice the layer thickness between parallel polarizers. Thus, in FIG. 17,aligning means 116 and 118 sandwich liquid crystal material 114.Reflective surface 134 on aligning means 118 operates together withsingle polarizer 136 which may be incorporated in aligning means 116. Itgives thus a wave-length independent full transmission for the samecondition (when the thickness corresponds to a relative phase change ofA'₂ to -A'₂ leading to outgoing amplitude A_(II) for ingoing A_(I) inone pass, cf. FIG. 18) as the transmissive device with crossedpolarizers gives wave-length independent extinction: with Ψ_(o) ≈22° asan example (FIG. 18) and the polarizer (P_(I)) set parallel to the n₁(e.g. :55) director state (white) the reflected intensity in the n₂(:66) state is given by I=I_(o) sin² 2πΔnd/λ, which would give (secondorder) blue characters against a white background for a layer thicknessof about 1 μm. Dark violet characters, fairly well approximating black,will result for a somewhat thinner layer. Strictly black, in the senseof extinction for all visible wavelengths would require two polarizers.With a different orientation, the single polarizer can also be used togive switching between two colors, rather between white and a color.

The reflective screen with one polarizer is somewhat brighter and has asuperior viewing angle as compared to a twisted nematic screen, and,since updating is required only if a pixel is to be changed, it would beextremely flicker-free, which is a condition hard to obtain with a CRT.The device would conveniently be built with an internal reflector. Ifthe reflective device ought to switch between black and color, a secondpolarizer is required, in crossed position behind the SSFLC layer(P_(II), FIG. 18). The brightness is now the same as for a twistednematic device, with viewing angle (and, of course, speed) stillstrongly advantageous.

For a screen with black letters on a white background, an attractivedesign would employ a 45° tilt material together with a black dichroicdye and in combination with only one polarizer. The polarizer can eitherbe in front or in the back. In the first case as illustrated in FIG. 17,the bright (non-absorbing) state as illustrated is switched to the darkone with directors oriented at 90° with respect to the directors in FIG.17, with a contrast ratio given by the ratio of transmissioncoefficients for the dichroic molecule oriented with its long axisrespectively normal to and along the optical electric field vector. Withthe polarizer behind the SSFLC layer (FIG. 19), unpolarized light entersthe cell, where the medium, with the directors oriented as illustrated,serves as a kind of polarizer admitting mainly vibrations parallel tothe polarizer (P) direction of polarizer 136. With the directors in theother position, the medium instead works as a polarizer crossed relativeto P. This last design not only gives excellent brightness and viewingangle, but permits the black characters to be perceived as being in theoutermost surface of the screen. Such a screen (which naturally shouldhave an anti-reflective coating) would therefore have a very appealingand pleasant appearance to the eye.

In connection with the development of non-emissive screens capable ofcolor, it is interesting to note an intrinsic advantage of SSFLCstructures in the reflective geometry with a single polarizer, namelythat, because there are two passes through the liquid crystal layerbetween polarizers, the birefringence colors are obtained which areoptimum with regard to saturation (the second order blue through thirdorder green), while maintaining the advantages of a thin liquid crystallayer (thickness ≈1 μm).

3. Color Devices

Devices are here discussed having one o,r more liquid crystal layers incombination with polarizers or filters to produce color when illuminatedin reflection or transmission. For reasons of simplicity, it is anadvantage if a color device can be made with just one layer of liquidcrystal.

One way of achieving a color screen in a single layer device is to usesome of the possible device structures giving continuouslyfield-variable birefringence (TUNABLE BIREFRINGENCE, cf. Section IX B1), and applying to each pixel, e.g. with a thin film transistor array,the voltage required for the color desired at any given time. Tunablebirefrigence is a method to produce colors well known in the art ofnematic liquid crystals, but only the use of the surface SSFLC switchingcan make the cells fast enough to permit development of multi-pixel ormatrix screens with sufficient contrast and viewing angle.

Another method of producing color on a screen, likewise well known inthe art, is to use the liquid crystal element as a shutter incombination with filter elements for the three primary colorsdistributed as an orderly array over the whole screen (T. Uchida, etal., Proceedings of the 1982 International Display Research Conference,SID/IEEE, pp. 166-170, 1982). For a screen in transmission mode theessential difference when replacing the nematic with the surfacestabilized ferroelectric will be increased speed and viewing angle. Fora screen in reflective mode an additional difference (apart fromtechnical details such as choice of different colors in the mesh) willbe that the SSFLC screen (one polarizer) will be brighter than thetwisted nematic screen by a factor T⁻², where T is the transmissioncoefficient for the polarizers used. This higher brightness is a generalfeature when SSFLC (operating in white/quasi-black mode) and TNreflective devices are compared.

A different approach to the color screen without using filters would usethe SSFLC geometry with nonhomogeneous bounding plates, as discussed inSection IX H 3, for example, just the DEVICE STRUCTURE of said patent,but with a varying sample thickness, which is just a juxtaposition ofmany devices of the kind described in said patent. Additionally, anyother device structure with uniform orientation could be similarlyemployed. In this design, every pixel would operate between a chosencolor state (any of the birefringence colors, including first orderwhite) and a black state (dark blue for the reflective case with asingle polarizer) but the local pixel color would vary due to aspatially varying liquid crystal layer thickness. A periodic variationin thickness can be obtained by evaporation of steps in two directions,e.g. in a constantly repeated 2×2 pixel array (FIG. 20a). Each such setof four pixels can then represent extinction or one of either fourcolors (1,2,3,4, e.g. 3 colors and white), or three colors (1,2,2,3),depending on whether or not the steps are unequal or equal in height inthe two directions. The color of different areas on the screen is nowgenerated by mixing or merging as in a common television tube: dependingon the observation distance to the screen, one has to make the colorpattern fine enough not to be resolved by the eye. The device will workequally well in reflective as in transmissive mode. Needless to say thearray unit does not have to be square (see FIG. 20d) and could be madewith a larger number of pixels, e.g. 4×4 (see FIGS. 20b and 20c)permitting more colors with finer resolution between them. Thus, in FIG.20b, liquid crystal 114 is between even thickness aligning means 116 andmulti-thickness aligning means 118 which has a basic unit of fourdifferent thicknesses in each of two directions.

Instead of using variable thickness, similar devices could employ anonhomogeneous selection of available surface states, such as discussedin Section IX B 1.

As pointed out in said patent, two ferroelectric layers sandwiched overone another and separately controlled give rise to 2×2 possibledifferent colors. The device in FIG. 21a has liquid crystal layers 114aand 114b in the same orientation between aligning means 116, 138 and 118and gives the four states indicated with two pairs of electrodes 140 and142, which in transmission between crossed polarizers in aligning means116 and 118 (one of the polarizers being perpendicular to the directorsin one of the states) would give one black (extinction) and threeprimary color states. It works equally well in reflection giving whiteplus three primary colors with just one front polarizer.

The same performance is achieved by the variation of FIG. 21b where thesmectic layers are tilted 2Ψ_(o), relative to each other so that onlyone of the director states is common to both. For this geometry however,another possibility may be pointed out (FIG. 22a): equipped with onlytwo electrodes (i.e. one pair--with no midway electrodes between thelayers, thus only driven by one electric field) both layers cooperate togive at least three distinct states, corresponding, in the case ofmonostable devices, to (1) no field, (2) down field and (3) up field.And they do this also in reflection with only one polarizer Furthermore,a substance with Ψ_(o) 45° and dichroic dye addition would, in the samemode, give rise to three "gray-scale" states of the color given by thedye (FIG. 22b). The devices can be made monostable using boundaryconditions enforcing a single molecular orientation at each surface,stabilizing the :55 state in one layer and the :66 state in the other.They can also be made multistable by employing switchable (e.g.,CIRCULAR CONICAL) boundary conditions with different thresholds for thetwo layers, making the :55-:55, :55-:66, :66-55, and :66-:66 states forthe two layers obtainable.

C. Devices with Multi-State Pixels

1. Twisted Smectic Devices

If a single-layer device is to produce any color, it has to have atleast three optically distinct states. Several one-layer devices withthis property can be found among the structures described in Section IXB 2, characterized by different boundary conditions on the two surfaces,and many variations of what we have termed TWISTED SMECTIC structuresare capable of at least three states.

One of the simplest twisted smectic device structures is depicted inFIG. 23. The lower and upper boundary directors, n₁ and n₂,respectively, are locked in two directions, for instance by SiOevaporation (cf. Section IV C), making the angle 2Ψ_(o), and theboundary conditions are assumed to be strong. In this geometry which isthe one of FIG. 8b, each smectic layer has a 180° change in φ from oneplate to the other. The field free (or weak field) state essentiallyguides the light polarization back and forth (cf. Section IX F) in adevice with internal or back reflector, which gives a certain color withconvenient setting of the front polarizer (such as in the generalarrangement in FIG. 17). With a strong applied up field, the directoreverywhere (except a thin boundary layer at top plate 116) will go intothe n₁ direction giving a second color. With a strong applied downfield, below the threshold for change of state at the bottom plate, thedirector everywhere (except a thin boundary layer at bottom plate 118)will go into the n₂ direction giving the third color. This color mayalso be achieved via a field-induced change of state at the bottomsurface for above threshold fields. Operation involving a state changewill be of advantage in multiplexed devices requiring maximalnonlinearity of response. In FIG. 23, Ψ_(o) has been chosen to be 45°without any limiting consequences for the discussion. The polarizationrotation angle is ≃2Ψ_(o) and could be changed by controlling thetemperature for a substance with a C-A transition.

Some twisted smectic devices, such as those of FIG. 10b, can be drivenas two-state devices and have advantages over the ones alreadydescribed, if the required function is the rotation of the polarizationplane in either the left or right sense depending on the applied field.

To mention one of the many further possibilities, suppose the bottom andtop plates were treated differently in order to make the switchingthreshold different at the two plates. It could, for instance, be madeby washing the bottom plate with acetone, while applying a hydrocarbontreatment to the upper one. Alternatively, one could use SiO evaporationin two directions (giving stable director orientations n₁, n₂) for thebottom plate and in one direction (n₃) at the top plate. In either casethere would be a strong tendency to enforce one of the cone directions 1and 2 in FIG. 24a at the bottom plate and a much weaker tendency at thetop plate, or even a tendency to prefer direction 3 if the torquesarising from the twist deformation in the director field were not toostrong. The general result is that the switching on the bottom surfaceoccurs at higher fields than on the top surface. This gives theswitching sequence that can be exemplified by FIG. 12a, with thedirector orientations in FIG. 24b, three of which, for instance (i),(ii), and (iii) can be achieved from one another in one step, while thetransitions between (i) and (iv) have to go via one of the other twostates.

2. Other Multi-State Devices

Color screens employing single liquid crystal layers can be devisedusing some of the possible device structures giving multiple states,each of which has uniform director orientation, for example the fourstate device of FIG. 11b, which presents four distinct orientations ofthe optic axis and thus can exhibit four distinct birefringence colors,one of which is extinction when employed in devices similar to FIGS. 16,17 and 19.

The multistate structures having some states of nonuniform orientationwill also yield distinct color effects when employed with one or twopolarizers. However, the multitude of possible cases renders anyindividual discussion impractical beyond what has been outlined inSection IX.

In general, controlled inhomogeneities in surface treatment or layertilt, as discussed in Section IX H 3, can be used to effectivelyincrease the number of states available in a multistate device.Consider, for example, a pair of pixels, a and b, both subject to thesame applied field, and both having the equilibrium structure of FIG.8b, but with pixel b having a weaker surface energy anisotropy and anoverall structure as illustrated in FIG. 16, 17 or 19. Then, as thefield is increased, as a pair (a-b) they will exhibit the followingsequences of five combined states: :66-:66, :66-:56, :56-:56, :56-:55,and :55-:55. Hence, the combination of two non-identical three statepixels with the same field applied yields a five state device. This isadvantageous in that it reduces in half the number of electricalconnections required to get five states over the case with identicalpixels.

D. Non-Matrix Arrays

One of the simplest applications, with essentially only one pixel (onelarge electrode) is an optical switch using total internal reflection.It is known in the art (R. A. Soref, Optics Letters, Volume 4, 155-157,1979, R. A. Soref. and D. H. McMahon, Optics Letters, Volume 5,147-149,1980), that the optic axis in a thin nematic liquid crystal layerbetween a pair of trapezoid prisms can be switched by an electric fieldso that a light ray is transmitted or totally reflected from theincident direction into another one, because of the change in theeffective index of refraction of the liquid crystal layer. A similar butmore rapid switch can be made with the SSFLC with the difference thatthe optic axis is rotated perpendicular to, and not in, the plane ofincidence. The angle of rotation is 2Ψ_(o). Thus, for a 45° substance,the effective interlayer refraction index can be changed, for apolarization perpendicular to the plane of incidence, by the amountn_(e) -n_(o), for Ψ_(o) <45° by a smaller amount. With a dichroic dyemixed in, the transmission could instead be changed for light having theorthogonal polarization. In contrast to any device using nematic liquidcrystals, like the one referred to above, or any other device knowntoday using other electro-optic materials, this device would satisfy tworequirements presently sought for in optical switches used in opticcommunications systems: (i) high switching speed (well above the kHzrange); and (ii) large refractive index change (Δn up to ≃0.3).

Another, in principle quite simple, but also one of the most attractivepossibilities for advanced application of SSFLCs is a sandwich offerroelectric liquid crystal and photoconductor acting as a light-lighttransducer, e.g. transforming incoherent light into coherent. For thisapplication, no complicated pattern of electrodes is necessary (or evendesirable) but the liquid crystal can either be in direct contact withthe photoconductor or in indirect contact via a thin evaporated surfacelayer for aligning purposes. In order to have an equally rapidbackswitching when a certain area is no longer illuminated, a small biasvoltage has to be applied to the sandwich.

Next in simplicity to those devices having only one pair, or a fewpairs, of electrodes, are linear array devices. These have aconsiderable potential in printing and copying applications and could,for instance, use pixels on a scale of 100 μm or finer resolution,arranged on a line containing 1000 pixels or more, covering the wholewidth of the text page, image or photograph that has to be printed. Alsoin this case the device has been demonstrated, but due to the slownessof the nematics used, the speed involved is at best ten times slowerthan a high speed xerox-type machine. With the resolution mentionedabove, and a switching time of 30 μS, which is even a fairlyconservative estimate for the surface stabilized ferroelectric liquidcrystal, the printing rate would instead be ≃3 meters/second, about 10times faster than the fastest xerox-type machine, corresponding to about1000 pages per minute. The pixels could be operated between two or morestates as a shutter for black and white pictures or, using the fasttunable birefringence, as switchable color filter points for producing acolor picture, e.g. by exposure to a photographic film. Because of thehigh rate of information transfer that is possible when a linear arrayis scanning a whole page in a single pass, instant black and white orcolor photos can be cabled from satellites or between continents or evenprojected on a luminescent screen in real time.

If the linear array is using two state pixels and if it is desired tostep up the shutter performance to controlling a gray scale,combinations of pixels can be used together with optics which combinethe light coming from several pixels, as exemplified by the cylindricallens 154 of FIG. 25. In FIG. 25, lens 154 combines the output of onepixel 150 with the output of a corresponding pixel 152. The two pixelsgive three levels of luminosity at the focal point. Four pixels wouldgive five levels but also require four electrical leads to each arrayelement. In this application, a combination of pixels with a singlecommon electrical connection but different switching thresholds, asdiscussed in Section X C 2, could be used to advantage. With the examplediscussed in Section X C 2 (combination of the N-P² pixels) arrayelements with five overall states could be addressed with a singlevoltage.

An altogether different design of a linear array is described in FIGS.26a and 26b. It employs a 45° tilt material with a dichroic dye andswitches between an absorbing and a non-absorbing state for light alongthe k direction. The electric field has to be applied along the bdirection by a set of inter-digitated electrode stripes 156 in FIG. 26b,the geometry of which defines the array. Each pixel could for instancemeasure 5×5 μm. This kind of design has the characteristic of not usingany polarizers at all. If used instead with electrode plates parallel tothe a-b plane this layer geometry may be used to control transmittedlight perpendicular to the applied electric field.

Finally, a method to produce color (cf. Section IX H 4) will bediscussed that, although of greater general applicability, may be mostpractical for a linear array. If a substance with a C-A transition isnot too far below the transition point, an applied heat pulse willchange the optic axis, according to FIG. 27a, from the actual n₁direction, say, to nearby direction n₁ ', shifted towards the state (n₃)representing the A phase. The idea is thus to use temperature as anadditional control variable which, in a sense, makes a pixel with twodevice states capable of becoming a multi-state pixel. The simplest caseis for n₁ '≈n₃ (it is unimportant whether the A phase is reached or onlyapproximated) giving three different states as in FIG. 27b. Bycontrolling what fraction of the time each pixel is in one of the threestates, any color can be produced, but the modulation of heat pulses canalso be performed such that advantage is taken of the continuous colorchanges possible. In fact, a TUNABLE BIREFRINGENCE situation existswhere the variable temperature controls color (by rotating n along anaxis parallel to the incoming light) in a way that is similar in itseffect as when the director is rotated continuously (though around anaxis perpendicular to the light beam) by changes in a controllingelectric field across a nematic liquid crystal. Thus, from the n₃ statethe medium goes back, in a monostable fashion, to whichever of n₁ and n₂has been preselected by the momentary electric field. For theapplication to matrix displays, the method of thermal switching betweenthe smectic F and C phases, already mentioned in section IX H 4, isprobably the more attractive one.

FIG. 28 illustrates an example of such a device. Attached to aligningmeans 116 are heating elements 154 overlayed with electrodes 156.Insulators 158 provide electrical isolation therebetween. Similarly,attached to aligning means 118 are heating elements 160 overlayed withelectrodes 162 and separated by insulators 164. As would be readilyapparent to those skilled in the art, heating elements 154 and 160 andelectrodes 156 and 162 may be positioned in any of a plethora ofpossible manners.

E. Design and Preparation of Cells

The device design and technology can be very different depending on thefunction and on the operational qualities desired of the device. Theapplications described in the last section in principle require onlysimple electrode patterns and, at least for most working conditions,relatively simple surface treatment. In other cases not only theelectrode configuration might be much more complicated, but also matchedby a complicated pattern in the surface treatment, permitting forinstance different switching properties on different regions of thesurface. In again other cases, the patterning of electrodes and of thesurface treatment may be combined so as to take advantage of the areanot used for switching to perform alignment functions over the activeelectrode areas. An example of this method will now be provided,employed to align the smectic C layers.

The method to be described combines two kinds of surface condition onthe plates with either an external field or the use of the A-C phasetransition. A different surface condition is employed at areas exteriorto the switchable (electrode) areas in order to control the layerdirection, but not the director, over the electrodes. FIG. 29illustrates this for parallel stripe electrodes 166 at a single surface118'. The surface treatment of the stripes is reduced to carefulcleaning by acetone (avoiding all surfactants) whereas areas 168 inbetween are evaporated obliquely with SiO in order to lock the directorin a certain direction (n₀), exemplified in the figure. (Top plate 116'can be treated correspondingly to give the same direction, n₀). Thedifference in surface treatment can be achieved by evaporation through amask, or by standard photolithographic techniques. If now the employedsubstance 114 has both a smectic A phase and a smectic C phase, the Aphase will grow with the layers perpendicular to the n₀ direction uponslow cooling from either the nematic or isotropic phase, establishingthis layer direction over the entire surface. In the latter case astrong stabilizing magnetic field should be applied along the n₀direction. On the other hand, over the electrodes, the director will gointo one of the switchable states given by the boundary conditionsthere. Thus, appropriately treating part of the surface for strongalignment, orients the smectic layers in a unique direction over theentire sample while permitting a high degree of director freedom overthe active (electrode) areas.

In the case that a smectic A phase is absent in compound 114, thetransition to the C phase from the nematic has to take place in thepresence of a DC electric field (10 to 50 volts over a couple ofmicrons) across the glass plates, because only the combination of themolecular orientation (n) and the direction of polarization (P) willdefine a unique direction of the smectic layer planes. If also thenematic phase is absent, the transition to the smectic C phase has to bedirectly from the isotropic phase in which case, again, a strongadditional magnetic field (parallel to n and perpendicular to E) will behelpful.

The electrode configuration can of course be chosen in a great number ofdifferent ways, and the switching properties will also depend on thelength scale of the array: for a sufficiently fine array, the switchingwill be monostable, but it will change to bistable for a sufficientlylarge array element dimension. For temperatures just below the A-Ctransition, one can expect the switching to be monostable for smallvalues of the tilt angle Ψ_(o) and flip to bistable for a Ψ_(o) greateror equal to a certain value (corresponding to a certain temperature).The SiO treated parts could further be along opaque stripes, likemetallic leads, or be on transparent areas.

A third variation of combined surface treatments, leading to apronounced bistability and memory is shown for a square array in FIG.30. Here pixels 170, which could be transparent or opaque, conductive ornonconductive, have received SiO treatment favoring horizontal director,thus aligning the A phase layers vertically whereas pixels 172 havereceived a double SiO treatment favoring each of the two tilt conedirections. If all pixels in the array are transparent and conductive,the two sets will have different switching properties which could beused to minimize crosstalk problems with even very simple addressingschemes.

Although a number of exemplary embodiments of this invention have beendescribed in detail above, those skilled in the art will readilyappreciate that many additional modifications are possible in theexemplary embodiments without materially departing from the novelteachings and advantages of this invention. Accordingly, all suchmodifications are intended to be included within the scope of thisinvention as defined in the following claims.

What is claimed is:
 1. An electro-optical reflector comprising:a pair ofsubstrates; a reflective surface associated with one of said substrates;chiral smectic liquid crystal material having a plurality of layers eachcomprised of a plurality of molecules, each molecule having a long axis,said long axes forming an angle other than 90° with said layers, saidliquid crystal material being disposed between said pair of substrates;said long axes of said molecules in a bulk of said liquid crystalmaterial forming helices, said substrates being spaced by a distancesufficiently small to suppress the formation of said helices; and meansfor applying an electric field to said liquid crystal material, saidelectric field causing said long axes to change orientation.
 2. Areflector as in claim 1, wherein said reflective surface is disposed onone of said substrates.
 3. A reflector as in claim 1, further comprisinga reflective layer disposed adjacent to one of said substrates, saidreflective surface being disposed on said reflective layer.
 4. Areflector as in claim 1, further comprising means for directing light topass through said liquid crystal material, reflect from said reflectivesurface, and pass through said liquid crystal material a second time. 5.A reflector as in claim 1 or 4 further comprising a polarizer whichpolarizes light passing through said liquid crystal material.
 6. Areflector as in claim 1 or 4 wherein said liquid crystal material isbirefringent and light passing through said liquid crystal material hasa wavelength, said birefringence producing optical retardance, saidsubstrates being spaced apart so that said retardance is one quarter ofsaid wavelength of said light upon each passage of said light throughsaid liquid crystal material.
 7. A liquid crystal device comprising:apair of substrates; chiral smectic liquid crystal material having aplurality of layers each comprised of a plurality of molecules, eachmolecule having a long axis, said long axes forming an angle other than90° with said layers, said layers aligned parallel to a direction in theplane of said substrates, said long axes of said molecules in a bulkforming helices, said liquid crystal material being disposed betweensaid pair of substrates which are spaced by a distance sufficientlysmall to suppress the formation of said helices; and means for applyingan electric field to said liquid crystal material, said electric fieldcausing said long axes to change orientation.
 8. A liquid crystal deviceas in claim 7, further comprising a reflective surface associated withone of said substrates.
 9. A liquid crystal device as in claim 8,wherein said reflective surface is one surface of said one of saidsubstrates.
 10. A liquid crystal device as in claim 7, furthercomprising means for directing light through said liquid crystalmaterial.
 11. A liquid crystal device comprising:a pair of substrates;birefringent chiral smectic liquid crystal material having a pluralityof layers each comprised of a plurality of molecules, each moleculehaving a long axis, said long axes forming an angle other than 90° withsaid layers, said long axes of said molecules in a bulk forming helices,said liquid crystal material being disposed between said pair ofsubstrates which are spaced by a distance sufficiently small to suppressthe formation of said helices; means for applying an electric field tosaid liquid crystal, said electric field causing said long axes tochange orientation; and means for directing light through said liquidcrystal material, said light having a wavelength, said birefringenceproducing optical retardance, said substrates being spaced apart so thatsaid retardance of said light passing through said liquid crystalmaterial is one-half of said wavelength of said light when said longaxes are in at least one orientation.
 12. A liquid crystal device as inclaim 11, wherein said directing means includes a reflective surfaceassociated with one of said substrates, said substrate spacing distancebeing that for which said retardance is one-quarter of said wavelengthof said light for each pass of said light through said liquid crystaldevice.
 13. A liquid crystal active matrix array comprising:a pair ofsubstrates; chiral smectic liquid crystal material having a plurality oflayers each comprised of a plurality of molecules, each molecule havinga long axis, said long axes forming an angle other than 90° with saidlayers, said layers aligned parallel to a direction in the plane of saidsubstrates, said long axes of said molecules in a bulk forming helices,said liquid crystal material being disposed between said pair ofsubstrates which are spaced by a distance sufficiently small to suppressthe formation of said helices; and means, including a transistor array,for selectively applying electric fields to portions of said liquidcrystal material, said electric fields causing said long axes of saidportions of said liquid crystal material to change orientation.
 14. Anarray as in claim 13, further comprising means for directing lightthrough said liquid crystal material.
 15. An array as in claim 13,further comprising a reflective surface associated with one of thesubstrates.
 16. An array as in claim 15, wherein said reflective surfaceis one surface of one of said substrates.
 17. A liquid crystal devicecomprisinga pair of substrates; chiral smectic liquid crystal materialhaving a plurality of layers each comprised of a plurality of molecules,each molecule having a long axis, said long axes forming an angle otherthan 90° with said layers, said layers aligned parallel to a directionin the plane of said substrates, said long axes of said molecules in abulk of said liquid crystal material forming helices, said liquidcrystal material being disposed between said pair of substrates whichare spaced by a distance sufficiently small to suppress the formation ofsaid helices; and means for applying an electric field to said liquidcrystal, said electric field causing said long axes to changeorientation, said change in orientation varying with said electric fieldin a continuous way.
 18. A device as in claim 17, further comprisingmeans for directing light through said liquid crystal material.
 19. Adevice as in claim 17, further comprising a reflective surfaceassociated with one of the substrates.
 20. A device as in claim 19,wherein said reflective surface is one surface of one of saidsubstrates.
 21. A twisted smectic liquid crystal device comprising:apair of substrates; chiral smectic liquid crystal material having aplurality of layers each comprised of a plurality of molecules, eachmolecule having a long axis, said long axes forming an angle other than90° with said layers, said layers aligned parallel to a direction in theplane of said substrates, said long axes of said molecules in a bulk ofsaid liquid crystal material forming helices, said liquid crystalmaterial being disposed between said pair of substrates which are spacedby a distance sufficiently small to suppress the formation of saidhelices; said substrates including means for inducing a twist in saidorientation of said long axes; and means for applying an electric fieldto said liquid crystal, said electric field causing said long axes tochange orientation.
 22. A device as in claim 21, wherein said change inorientation varies with said electric field in a continuous way.
 23. Adevice as in claim 21 or 22 further comprising means for directing lightthrough said liquid crystal material.
 24. A device as in claim 21 or 22,further comprising a reflective surface associated with one of saidsubstrates.
 25. A device as in claim 24, wherein said reflective surfaceis one surface of one of said substrates.